| 1. |
- Elfverson, Daniel, et al.
(författare)
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Multiscale methods for problems with complex geometry
- 2017
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 321, s. 103-123
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Tidskriftsartikel (refereegranskat)abstract
- We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We construct corrected coarse test and trail spaces which takes the fine scale features of the computational domain into account. The corrections only need to be computed in regions surrounding fine scale geometric features. We achieve linear convergence rate in the energy norm for the multiscale solution. Moreover, the conditioning of the resulting matrices is not affected by the way the domain boundary cuts the coarse elements in the background mesh. The analytical findings are verified in a series of numerical experiments.
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| 2. |
- Johansson, August, et al.
(författare)
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High order cut finite element methods for the Stokes problem
- 2015
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Ingår i: Advanced Modeling and Simulation in Engineering Sciences. - : Springer. - 2213-7467. ; 2:1, s. 1-23
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Tidskriftsartikel (refereegranskat)abstract
- We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on a Nitsche formulation of the interface condition together with a stabilization term. Starting from inf-sup stable spaces on the two meshes, we prove that the resulting composite method is indeed inf-sup stable and as a consequence optimal a priori error estimates hold.
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| 3. |
- Larsson, Karl, 1981-, et al.
(författare)
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A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces
- 2017
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Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 86:308, s. 2613-2649
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Tidskriftsartikel (refereegranskat)abstract
- We present a continuous/discontinuous Galerkin method for approximating solutions to a fourth order elliptic PDE on a surface embedded in R-3. A priori error estimates, taking both the approximation of the surface and the approximation of surface differential operators into account, are proven in a discrete energy norm and in L-2 norm. This can be seen as an extension of the formalism and method originally used by Dziuk ( 1988) for approximating solutions to the Laplace-Beltrami problem, and within this setting this is the first analysis of a surface finite element method formulated using higher order surface differential operators. Using a polygonal approximation inverted right perpendicular(h) of an implicitly defined surface inverted right perpendicular we employ continuous piecewise quadratic finite elements to approximate solutions to the biharmonic equation on inverted right perpendicular. Numerical examples on the sphere and on the torus confirm the convergence rate implied by our estimates.
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| 4. |
- Massing, André, et al.
(författare)
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A Nitsche-Based Cut Finite Element Method for a Fluid--Structure Interaction Problem
- 2015
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Ingår i: Communications in Applied Mathematics and Computational Science. - : Mathematical Sciences Publishers. - 1559-3940 .- 2157-5452. ; 10:2, s. 97-120
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Tidskriftsartikel (refereegranskat)abstract
- We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.
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| 5. |
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