| 1. |
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| 2. |
- Lembrechts, Jonas J., et al.
(författare)
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SoilTemp : A global database of near-surface temperature
- 2020
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Ingår i: Global Change Biology. - : Wiley. - 1354-1013 .- 1365-2486. ; 26:11, s. 6616-6629
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Tidskriftsartikel (refereegranskat)abstract
- Current analyses and predictions of spatially explicit patterns and processes in ecology most often rely on climate data interpolated from standardized weather stations. This interpolated climate data represents long-term average thermal conditions at coarse spatial resolutions only. Hence, many climate-forcing factors that operate at fine spatiotemporal resolutions are overlooked. This is particularly important in relation to effects of observation height (e.g. vegetation, snow and soil characteristics) and in habitats varying in their exposure to radiation, moisture and wind (e.g. topography, radiative forcing or cold-air pooling). Since organisms living close to the ground relate more strongly to these microclimatic conditions than to free-air temperatures, microclimatic ground and near-surface data are needed to provide realistic forecasts of the fate of such organisms under anthropogenic climate change, as well as of the functioning of the ecosystems they live in. To fill this critical gap, we highlight a call for temperature time series submissions to SoilTemp, a geospatial database initiative compiling soil and near-surface temperature data from all over the world. Currently, this database contains time series from 7,538 temperature sensors from 51 countries across all key biomes. The database will pave the way toward an improved global understanding of microclimate and bridge the gap between the available climate data and the climate at fine spatiotemporal resolutions relevant to most organisms and ecosystem processes.
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| 3. |
- Palmerio, Erika, et al.
(författare)
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CMEs and SEPs During November-December 2020 : A Challenge for Real-Time Space Weather Forecasting
- 2022
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Ingår i: Space Weather. - : American Geophysical Union (AGU). - 1542-7390. ; 20:5
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Tidskriftsartikel (refereegranskat)abstract
- Predictions of coronal mass ejections (CMEs) and solar energetic particles (SEPs) are a central issue in space weather forecasting. In recent years, interest in space weather predictions has expanded to include impacts at other planets beyond Earth as well as spacecraft scattered throughout the heliosphere. In this sense, the scope of space weather science now encompasses the whole heliospheric system, and multipoint measurements of solar transients can provide useful insights and validations for prediction models. In this work, we aim to analyze the whole inner heliospheric context between two eruptive flares that took place in late 2020, that is, the M4.4 flare of 29 November and the C7.4 flare of 7 December. This period is especially interesting because the STEREO-A spacecraft was located similar to 60 degrees east of the Sun-Earth line, giving us the opportunity to test the capabilities of "predictions at 360 degrees" using remote-sensing observations from the Lagrange L1 and L5 points as input. We simulate the CMEs that were ejected during our period of interest and the SEPs accelerated by their shocks using the WSA-Enlil-SEPMOD modeling chain and four sets of input parameters, forming a "mini-ensemble." We validate our results using in situ observations at six locations, including Earth and Mars. We find that, despite some limitations arising from the models' architecture and assumptions, CMEs and shock-accelerated SEPs can be reasonably studied and forecast in real time at least out to several tens of degrees away from the eruption site using the prediction tools employed here.
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| 4. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A finite element method with discontinuous rotations for the Mindlin-Reissner plate model
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:5-8, s. 638-648
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Tidskriftsartikel (refereegranskat)abstract
- We present a continuous-discontinuous finite element method for the Mindlin-Reissner plate model based on continuous polynomials of degree k >= 2 for the transverse displacements and discontinuous polynomials of degree k - 1 for the rotations. We prove a priori convergence estimates, uniformly in the thickness of the plate, and thus show that locking is avoided. We also derive a posteriori error estimates based on duality, together with corresponding adaptive procedures for controlling linear functionals of the error. Finally, we present some numerical results.
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| 5. |
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| 6. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-Love plate
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - Amsterdam : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:47-48, s. 3289-3295
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Tidskriftsartikel (refereegranskat)abstract
- We present energy norm a posteriori error estimates for continuous/discontinuous Galerkin (c/dG) approximations of the Kirchhoff-Love plate problem. The method is based on a continuous displacement field inserted into a symmetric discontinuous Galerkin formulation of the fourth order partial differential equation governing the deflection of a thin plate. We also give explicit formulas for the penalty parameter involved in the formulation.
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| 7. |
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| 8. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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An adaptive finite element method for second order plate theory
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 81:5, s. 584-603
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Tidskriftsartikel (refereegranskat)abstract
- We present a discontinuous finite element method for the Kirchhoff plate model with membrane stresses. The method is based on P2-approximations on simplices for the out-of-plane deformations, using C0-continuous approximations. We derive a posteriori error estimates for linear functionals of the error and give some numerical examples.
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| 9. |
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| 10. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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Energy norm a posteriori error estimates for discontinuous Galerkin approximations of the linear elasticity problem
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - Amsterdam : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:45-46, s. 3026-3030
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Tidskriftsartikel (refereegranskat)abstract
- We present a residual-based a posteriori error estimate in an energy norm of the error in a family of discontinuous Galerkin approximations of linear elasticity problems. The theory is developed in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
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| 11. |
- Hansbo, Peter F G, 1959, et al.
(författare)
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Piecewise divergence free discontinuous Galerkin methods
- 2008
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Ingår i: Communications in Numerical Methods in Engineering. - : Wiley. - 1069-8299 .- 1099-0887. ; 24:5, s. 355-366
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix-Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions.
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| 12. |
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| 13. |
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| 14. |
- Lembrechts, Jonas J., et al.
(författare)
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Global maps of soil temperature
- 2022
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Ingår i: Global Change Biology. - : Wiley. - 1354-1013 .- 1365-2486. ; 28:9, s. 3110-3144
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Tidskriftsartikel (refereegranskat)abstract
- Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km2 resolution for 0–5 and 5–15cm soil depth. These maps were created by calculating the difference (i.e. offset) between in situ soil temperature measurements, based on time series from over 1200 1-km2 pixels (summarized from 8519 unique temperature sensors) across all the world's major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean=3.0±2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6±2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (−0.7±2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications.
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| 15. |
- Araujo-Cabarcas, Juan Carlos, 1981-
(författare)
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Reliable hp finite element computations of scattering resonances in nano optics
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Eigenfrequencies are commonly studied in wave propagation problems, as they are important in the analysis of closed cavities such as a microwave oven. For open systems, energy leaks into infinity and therefore scattering resonances are used instead of eigenfrequencies. An interesting application where resonances take an important place is in whispering gallery mode resonators.The objective of the thesis is the reliable and accurate approximation of scattering resonances using high order finite element methods. The discussion focuses on the electromagnetic scattering resonances in metal-dielectric nano-structures using a Drude-Lorentz model for the description of the material properties. A scattering resonance pair satisfies a reduced wave equationand an outgoing wave condition. In this thesis, the outgoing wave condition is replaced by a Dirichlet-to-Neumann map, or a Perfectly Matched Layer. For electromagnetic waves and for acoustic waves, the reduced wave equation is discretized with finite elements. As a result, the scattering resonance problem is transformed into a nonlinear eigenvalue problem.In addition to the correct approximation of the true resonances, a large number of numerical solutions that are unrelated to the physical problem are also computed in the solution process. A new method based on a volume integral equation is developed to remove these false solutions.The main results of the thesis are a novel method for removing false solutions of the physical problem, efficient solutions of non-linear eigenvalue problems, and a new a-priori based refinement strategy for high order finite element methods. The overall material in the thesis translates into a reliable and accurate method to compute scattering resonances in physics and engineering.
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| 16. |
- Becker, Roland, et al.
(författare)
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Energy norm a posteriori error estimation for discontinuous Galerkin methods
- 2003
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825 .- 1879-2138. ; 192:5-6, s. 723-733
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.
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| 17. |
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| 18. |
- Bengzon, Fredrik, 1978-, et al.
(författare)
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Adaptive finite element approximation of multiphysics problems : a fluid structure interaction model problem
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 84:12, s. 1451-1465
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Tidskriftsartikel (refereegranskat)abstract
- We consider computation of the displacement of an elastic object immersed into a viscous incompressible flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. We derive an a posteriori error estimate for this one way coupled problem using duality techniques. Based on these estimates we develop an adaptive algorithm that automatically constructs a suitable adapted mesh for the fluid and solid domains given goal quantities specified on the solid problem.
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| 19. |
- Bengzon, Fredrik, 1978-, et al.
(författare)
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Adaptive piecewise constant discontinuous Galerkin methods for convection-diffusion problems
- 2009
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present a discontinuous Galerkin method with piecewise constant approximation for convection-diffusion type equations. We show that if the discretization is carefully chosen, then the method is optimal in the L2 norm as well as in a discrete energy norm measuring the normal flux across element boundaries. We also derive a posteriori error estimates and illustrate their effectiveness in combination with adaptive mesh refinement on a few benchmark problems.
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| 20. |
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| 21. |
- Bengzon, Fredrik, 1978-, et al.
(författare)
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Simulation of multiphysics problems using adaptive finite elements
- 2006
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Ingår i: Applied parallel computing state of the art in scientific computing. - umeå : department of Mathematics, Umeå University. ; , s. 1-14
-
Konferensbidrag (refereegranskat)abstract
- Real world applications often involve several types of physics. In practice, one often solves such multiphysics problems by using already existing single physics solvers. To satisfy an overall accuracy, it is critical to understand how accurate the individual single physics solution must be. In this paper we present a framework for a posteriori error estimation of multiphysics problems and derive an algorithm for estimating the total error. We illustrate the technique by solving a coupled flow and transport problem with application in porous media flow.
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| 22. |
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| 23. |
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| 24. |
- Bensow, Rickard, 1972, et al.
(författare)
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Residual Based VMS Subgrid Modeling for Vortex Flows
- 2009
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 199:13-16, s. 802-809
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a residual based subgrid modeling approach for Large Eddy Simulations (LES) based on the variational multiscale method as a cure for the problem of preservation of vortices in numerical flow simulation. This approach combines a splitting of the non-linear term in the Navier–Stokes equations into strain and vorticity with a residual based modeling of the subgrid problems. The benefit is that certain driving phenomena, normally not present in subgrid modeling, e.g. vortex stretching, can be seen in the equations.Here, we focus on two of the subgrid terms arising from the subgrid scale problem. The effect of the two terms are illustrated in an LES of a three dimensional flow around a wing where the main feature is the formation and preservation of a tip vortex, an important phenomenon in many aerodynamic and hydrodynamical applications. We see that the addition of the new subgrid terms correctly counteracts the dissipative effect, arising from numerics and turbulence modeling, on the vortex and thus strongly improves prediction of the tip vortex.
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| 25. |
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| 26. |
- Björklund, Martin, et al.
(författare)
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Error estimates for finite element approximations of viscoelastic dynamics : the generalized Maxwell model
- 2024
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 425
-
Tidskriftsartikel (refereegranskat)abstract
- We prove error estimates for a finite element approximation of viscoelastic dynamics based on continuous Galerkin in space and time, both in energy norm and in L2 norm. The proof is based on an error representation formula using a discrete dual problem and a stability estimate involving the kinetic, elastic, and viscoelastic energies. To set up the dual error analysis and to prove the basic stability estimates, it is natural to formulate the problem as a first-order-in-time system involving evolution equations for the viscoelastic stress, the displacements, and the velocities. The equations for the viscoelastic stress can, however, be solved analytically in terms of the deviatoric strain velocity, and therefore, the viscoelastic stress can be eliminated from the system, resulting in a system for displacements and velocities.
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| 27. |
- Boiveau, Thomas, et al.
(författare)
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Fictitious domain method with boundary value correction using penalty-free Nitsche method
- 2018
-
Ingår i: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 26:2, s. 77-95
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by ?(h1/2) in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.
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| 28. |
- Burman, Erik, et al.
(författare)
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A cut discontinuous Galerkin method for the Laplace–Beltrami operator
- 2017
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Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press. - 0272-4979 .- 1464-3642. ; 37:1, s. 138-169
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Tidskriftsartikel (refereegranskat)abstract
- We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in R. The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in R. The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.
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| 29. |
- Burman, Erik, et al.
(författare)
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A cut finite element method for a model of pressure in fractured media
- 2020
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Ingår i: Numerische Mathematik. - : Springer. - 0029-599X .- 0945-3245. ; 146:4, s. 783-818
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Tidskriftsartikel (refereegranskat)abstract
- We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: (1) Stability of the formulation in the full range of parameter choices; and (2) Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.
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| 30. |
- Burman, Erik, et al.
(författare)
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A cut finite element method for elliptic bulk problems with embedded surfaces
- 2019
-
Ingår i: GEM - International Journal on Geomathematics. - : Springer. - 1869-2672 .- 1869-2680. ; 10:1
-
Tidskriftsartikel (refereegranskat)abstract
- We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace–Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.
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| 31. |
- Burman, Erik, et al.
(författare)
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A cut finite element method for the Bernoulli free boundary value problem
- 2017
-
Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 317, s. 598-618
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Tidskriftsartikel (refereegranskat)abstract
- We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion. This leads to so called cut elements in the vicinity of the boundary. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements penalizing the gradient jumps across element sides. The stabilization also ensures good conditioning of the resulting discrete system. We develop a method for shape optimization based on moving the distance function along a velocity field which is computed as the H1 Riesz representation of the shape derivative. We show that the velocity field is the solution to an interface problem and we prove an a priori error estimate of optimal order, given the limited regularity of the velocity field across the interface, for the velocity field in the H1norm. Finally, we present illustrating numerical results.
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| 32. |
- Burman, Erik, et al.
(författare)
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A cut finite element method with boundary value correction
- 2018
-
Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:310, s. 633-657
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Tidskriftsartikel (refereegranskat)abstract
- In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee in [Math. Comp. 26 (1972), 869-879]. The cut finite element method is a fictitious domain method with Nitsche-type enforcement of Dirich-let conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.
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| 33. |
- Burman, Erik, et al.
(författare)
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A posteriori error estimates with boundary correction for a cut finite element method
- 2022
-
Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press. - 0272-4979 .- 1464-3642. ; 42:1, s. 333-362
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Tidskriftsartikel (refereegranskat)abstract
- In this work we introduce, analyze and implement a residual-based a posteriori error estimation for the CutFEM fictitious domain method applied to an elliptic model problem. We consider the problem with smooth (nonpolygonal) boundary and, therefore, the analysis takes into account both the geometry approximation error on the boundary and the numerical approximation error. Theoretically, we can prove that the error estimation is both reliable and efficient. Moreover, the error estimation is robust in the sense that both the reliability and efficiency constants are independent of the arbitrary boundary-mesh intersection.
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| 34. |
- Burman, Erik, et al.
(författare)
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A simple approach for finite element simulation of reinforced plates
- 2018
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Ingår i: Finite elements in analysis and design (Print). - : Elsevier. - 0168-874X .- 1872-6925. ; 142, s. 51-60
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Tidskriftsartikel (refereegranskat)abstract
- We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the plate elements. This allows for a fast and easy way of assessing where the plate should be supported, for instance, in an optimization loop.
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| 35. |
- Burman, Erik, et al.
(författare)
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A simple finite element method for elliptic bulk problems with embedded surfaces
- 2019
-
Ingår i: Computational Geosciences. - : Springer. - 1420-0597 .- 1573-1499. ; 23:1, s. 189-199
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the mesh in arbitrary fashion and we take the flow in the crack into account by superposition. The fact that we use continuous elements leads to suboptimal convergence due to the loss of regularity across the crack. We therefore refine the mesh in the vicinity of the crack in order to recover optimal order convergence in terms of the global mesh parameter. The proper degree of refinement is determined based on an a priori error estimate and can thus be performed before the actual finite element computation is started. Numerical examples showing this effect and confirming the theoretical results are provided. The approach is easy to implement and beneficial for rapid assessment of the effect of crack orientation and may for example be used in an optimization loop.
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| 36. |
- Burman, Erik, et al.
(författare)
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A stabilized cut finite element method for partial differential equations on surfaces : The Laplace-Beltrami operator
- 2015
-
Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 285, s. 188-207
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Tidskriftsartikel (refereegranskat)abstract
- We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. The resulting discrete method may be severely ill-conditioned, and the main purpose of this paper is to suggest a remedy for this problem based on adding a consistent stabilization term to the original bilinear form. We show optimal estimates for the condition number of the stabilized method independent of the location of the surface. We also prove optimal a priori error estimates for the stabilized method. (c) 2014 Elsevier B.V. All rights reserved.
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| 37. |
- Burman, Erik, et al.
(författare)
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A stabilized cut streamline diffusion finite element method for convection–diffusion problems on surfaces
- 2020
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 358
-
Tidskriftsartikel (refereegranskat)abstract
- We develop a stabilized cut finite element method for the stationary convection–diffusion problem on a surface embedded in Rd. The cut finite element method is based on using an embedding of the surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the standard piecewise linear continuous elements to a piecewise linear approximation of the surface. The stabilization consists of a standard streamline diffusion stabilization term on the discrete surface and a so called normal gradient stabilization term on the full tetrahedral elements in the active mesh. We prove optimal order a priori error estimates in the standard norm associated with the streamline diffusion method and bounds for the condition number of the resulting stiffness matrix. The condition number is of optimal order for a specific choice of method parameters. Numerical examples supporting our theoretical results are also included.
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| 38. |
- Burman, E., et al.
(författare)
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A stable cut finite element method for partial differential equations on surfaces : The Helmholtz–Beltrami operator
- 2020
-
Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 362
-
Tidskriftsartikel (refereegranskat)abstract
- We consider solving the surface Helmholtz equation on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. Using a stabilized method combining Galerkin least squares stabilization and a penalty on the gradient jumps we obtain stability of the discrete formulation under the condition hk<C, where h denotes the mesh size, k the wave number and C a constant depending mainly on the surface curvature κ, but not on the surface/mesh intersection. Optimal error estimates in the H1 and L2-norms follow.
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| 39. |
- Burman, Erik, et al.
(författare)
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Augmented Lagrangian and Galerkin least-squares methods for membrane contact
- 2018
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 114:11, s. 1179-1191
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations.
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| 40. |
- Burman, Erik, et al.
(författare)
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Augmented Lagrangian finite element methods for contact problems
- 2019
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Ingår i: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 53:1, s. 173-195
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Tidskriftsartikel (refereegranskat)abstract
- We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.
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| 41. |
- Burman, E., et al.
(författare)
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Augmented Lagrangian Method for Thin Plates with Signorini Boundaries
- 2021
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Ingår i: Numerical Mathematics and Advanced Applications ENUMATH 2019. - Cham : Springer. - 9783030558734 - 9783030558741 - 9783030558765 ; , s. 509-519
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Konferensbidrag (refereegranskat)abstract
- We consider C1-continuous approximations of the Kirchhoff plate problem in combination with a mesh dependent augmented Lagrangian method on a simply supported Signorini boundary.
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| 42. |
- Burman, Erik, et al.
(författare)
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Comparison of Shape Derivatives Using CutFEM for Ill-posed Bernoulli Free Boundary Problem
- 2021
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Ingår i: Journal of Scientific Computing. - : Springer Nature. - 0885-7474 .- 1573-7691. ; 88:2
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study and compare three types of shape derivatives for free boundary identification problems. The problem takes the form of a severely ill-posed Bernoulli problem where only the Dirichlet condition is given on the free (unknown) boundary, whereas both Dirichlet and Neumann conditions are available on the fixed (known) boundary. Our framework resembles the classical shape optimization method in which a shape dependent cost functional is minimized among the set of admissible domains. The position of the domain is defined implicitly by the level set function. The steepest descent method, based on the shape derivative, is applied for the level set evolution. For the numerical computation of the gradient, we apply the Cut Finite Element Method (CutFEM), that circumvents meshing and re-meshing, without loss of accuracy in the approximations of the involving partial differential models. We consider three different shape derivatives. The first one is the classical shape derivative based on the cost functional with pde constraints defined on the continuous level. The second shape derivative is similar but using a discretized cost functional that allows for the embedding of CutFEM formulations directly in the formulation. Different from the first two methods, the third shape derivative is based on a discrete formulation where perturbations of the domain are built into the variational formulation on the unperturbed domain. This is realized by using the so-called boundary value correction method that was originally introduced to allow for high order approximations to be realized using low order approximation of the domain. The theoretical discussion is illustrated with a series of numerical examples showing that all three approaches produce similar result on the proposed Bernoulli problem.
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| 43. |
- Burman, Erik, et al.
(författare)
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Cut Bogner-Fox-Schmit elements for plates
- 2020
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Ingår i: Advanced Modeling and Simulation in Engineering Sciences. - : Springer. - 2213-7467. ; 7:1
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Tidskriftsartikel (refereegranskat)abstract
- We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are C1 elements obtained by taking tensor products of Hermite splines. The formulation is based on Nitsche’s method for weak enforcement of essential boundary conditions together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system of linear equations. We also take geometric approximation of the boundary into account and we focus our presentation on the simply supported boundary conditions which is the most sensitive case for geometric approximation of the boundary.
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| 44. |
- Burman, Erik, et al.
(författare)
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Cut finite element methods for coupled bulk–surface problems
- 2016
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Ingår i: Numerische Mathematik. - : Springer. - 0029-599X .- 0945-3245. ; 133:2, s. 203-231
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Tidskriftsartikel (refereegranskat)abstract
- We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and (Formula presented.) norms of the error. Using stabilization terms we show that the resulting algebraic system of equations has a similar condition number as a standard fitted finite element method. Finally, we present a numerical example illustrating the accuracy and the robustness of our approach.
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| 45. |
- Burman, Erik, et al.
(författare)
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Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions
- 2019
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Ingår i: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 52:6, s. 2247-2282
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Tidskriftsartikel (refereegranskat)abstract
- We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in Rd of arbitrary codimension. The method is based on using continuous piecewise linears on a background mesh in the embedding space for approximation together with a stabilizing form that ensures that the resulting problem is stable. The discrete manifold is represented using a triangulation which does not match the background mesh and does not need to be shape-regular, which includes level set descriptions of codimension one manifolds and the non-matching embedding of independently triangulated manifolds as special cases. We identify abstract key assumptions on the stabilizing form which allow us to prove a bound on the condition number of the stiffness matrix and optimal order a priori estimates. The key assumptions are verified for three different realizations of the stabilizing form including a novel stabilization approach based on penalizing the surface normal gradient on the background mesh. Finally, we present numerical results illustrating our results for a curve and a surface embedded in R3.
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| 46. |
- Burman, Erik, et al.
(författare)
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Cut finite elements for convection in fractured domains
- 2019
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Ingår i: Computers & Fluids. - : Elsevier. - 0045-7930 .- 1879-0747. ; 179, s. 728-736
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Tidskriftsartikel (refereegranskat)abstract
- We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain, which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.
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| 47. |
- Burman, Erik, et al.
(författare)
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Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions
- 2019
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 350, s. 462-479
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Tidskriftsartikel (refereegranskat)abstract
- We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represent parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche's method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero.
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| 48. |
- Burman, Erik, et al.
(författare)
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CutFEM : Discretizing geometry and partial differential equations
- 2015
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 104:7, s. 472-501
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Tidskriftsartikel (refereegranskat)abstract
- We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.
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| 49. |
- Burman, Erik, et al.
(författare)
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CutFEM based on extended finite element spaces
- 2022
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Ingår i: Numerische Mathematik. - : Springer. - 0029-599X .- 0945-3245. ; 152, s. 331-369
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Tidskriftsartikel (refereegranskat)abstract
- We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected by the boundary occur and these elements must in general by stabilized in some way. Discrete extension operators provides such a stabilization by modification of the finite element space close to the boundary. More, precisely the finite element space is extended from the stable interior elements over the boundary in a stable way which also guarantees optimal approximation properties. Our framework is applicable to all standard nodal based finite elements of various order and regularity. We develop an abstract theory for elliptic problems and associated parabolic time dependent partial differential equations and derive a priori error estimates. We finally apply this to some examples of partial differential equations of different order including the interface problems, the biharmonic operator and the sixth order triharmonic operator.
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| 50. |
- Burman, Erik, et al.
(författare)
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Dirichlet boundary value correction using Lagrange multipliers
- 2020
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Ingår i: BIT Numerical Mathematics. - : Springer. - 0006-3835 .- 1572-9125. ; 60:1, s. 235-260
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Tidskriftsartikel (refereegranskat)abstract
- We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to a Taylor series expansion approach previously used in the context of Nitsche's method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.
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