| 1. |
- Bengzon, Fredrik, 1978-, et al.
(author)
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Simulation of multiphysics problems using adaptive finite elements
- 2006
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In: Applied parallel computing state of the art in scientific computing. - umeå : department of Mathematics, Umeå University. ; , s. 1-14
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Conference paper (peer-reviewed)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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| 2. |
- Larson, Mats G., et al.
(author)
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Adaptive submodeling for linear elasticity problems with multiscale geometric features
- 2005
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In: Multiscale Methods in Science and Engineering. - Berlin Heidelberg : Springer Verlag. - 9783540253358 - 9783540264446 ; , s. 169-180
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Book chapter (other academic/artistic)abstract
- Submodeling is a procedure for local enhancement of the resolution of a coarse global finite element solution by solving a local problem on a subdomain containing an area of particular interest. We focus on linear elasticity and computation of local stress levels determined by the local geometry of the domain. We derive a posteriori error estimates for the submodeling procedure using duality techniques. Based on these estimates we propose an adaptive procedure for automatic choice of the resolution and size of the submodel. The procedure is illustrated for problems of industrial interest.
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| 3. |
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| 4. |
- Bengzon, Fredrik, 1978-, et al.
(author)
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Adaptive finite element approximation of multiphysics problems : a fluid structure interaction model problem
- 2010
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In: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 84:12, s. 1451-1465
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Journal article (peer-reviewed)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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| 5. |
- Bengzon, Fredrik, 1978-
(author)
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Adaptive finite element methods for multiphysics problems
- 2009
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Doctoral thesis (other academic/artistic)abstract
- In this thesis we develop and analyze the performance ofadaptive finite element methods for multiphysics problems. Inparticular, we propose a methodology for deriving computable errorestimates when solving unidirectionally coupled multiphysics problemsusing segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard frameworkof dual weighted residual estimates. A main feature of themethodology is its capability of automatically estimating thepropagation of error between the involved solvers with respect to anoverall computational goal. The a posteriori estimates are used todrive local mesh refinement, which concentrates the computationalpower to where it is most needed. We have applied and numericallystudied the methodology to several common multiphysics problems usingvarious types of finite elements in both two and three spatialdimensions. Multiphysics problems often involve convection-diffusion equations for whichstandard finite elements can be unstable. For such equations we formulatea robust discontinuous Galerkin method of optimal order with piecewiseconstant approximation. Sharp a priori and a posteriori error estimatesare proved and verified numerically. Fractional step methods are popular for simulating incompressiblefluid flow. However, since they are not genuine Galerkin methods, butrather based on operator splitting, they do not fit into the standardframework for a posteriori error analysis. We formally derive an aposteriori error estimate for a prototype fractional step method byseparating the error in a functional describing the computational goalinto a finite element discretization residual, a time steppingresidual, and an algebraic residual.
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| 6. |
- Bengzon, Fredrik, 1978-, et al.
(author)
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Adaptive piecewise constant discontinuous Galerkin methods for convection-diffusion problems
- 2009
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Other publication (other academic/artistic)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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| 7. |
- Larson, Mats G, et al.
(author)
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Adaptive finite element approximation of coupled flow and transport problems with applications in heat transfer
- 2008
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In: International Journal for Numerical Methods in Fluids. - : Wiley. - 0271-2091 .- 1097-0363. ; 57:9, s. 1397-1420
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Journal article (peer-reviewed)abstract
- In this paper we develop an adaptive finite element method for heat transfer in incompressible fluid flow. The adaptive method is based on an a posteriori error estimate for the coupled problem, which identifies how accurately the flow and heat transfer problems must be solved in order to achieve overall accuracy in a specified goal quantity. The a posteriori error estimate is derived using duality techniques and is of dual weighted residual type. We consider, in particular, an a posteriori error estimate for a variational approximation of the integrated heat flux through the boundary of a hot object immersed into a cooling fluid flow. We illustrate the method on some test cases involving three-dimensional time-dependent flow and transport.
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| 8. |
- Larson, Mats G., et al.
(author)
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Adaptive finite element approximation of multiphysics problems
- 2007
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In: Communications in Numerical Methods in Engineering. - : Wiley InterScience. - 1069-8299 .- 1099-0887. ; 24:6, s. 505-521
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Journal article (peer-reviewed)abstract
- Simulation of multiphysics problems is a common task in applied research and industry. Often a multiphysics solver is built by connecting several single-physics solvers into a network. In this paper, we develop a basic adaptive methodology for such multiphysics solvers. The adaptive methodology is based on a posteriori error estimates that capture the influence of the discretization errors in the different solvers on a given functional output. These estimates are derived using duality-based techniques.
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