Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model

We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one o...

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Published in:Journal of computational methods in applied mathematics Vol. 17; no. 3; pp. 377 - 396
Main Authors: Bærland, Trygve, Lee, Jeonghun J., Mardal, Kent-Andre, Winther, Ragnar
Format: Journal Article
Language:English
Published: Minsk De Gruyter 01.07.2017
Walter de Gruyter GmbH
Subjects:
65N30
65N55
74S05
Computational fluid dynamics
Conditioning
Consolidation
Discretization
Elasticity
Finite element method
Finite Elements
Mathematical models
Parameters
Poroelasticity
Preconditioning
Robustness
Tensors
ISSN:1609-4840, 1609-9389
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Abstract We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are well-conditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.
AbstractList We discuss the construction of robust preconditioners for finite element approximationsof Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based ongeneralizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor isone of the unknowns. The Biot model has a number of applications in science, medicine, and engineering.A challenge in many of these applications is that the model parameters range over several orders of magnitude.Therefore, discretization procedures which are well behaved with respect to such variations are needed.The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discretesystems are well-conditioned with respect to variations of the model parameters as well as refinements ofthe discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.
We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are well-conditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.
We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger–Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are well-conditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.
Author Lee, Jeonghun J.
Winther, Ragnar
Mardal, Kent-Andre
Bærland, Trygve
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  surname: Winther
  fullname: Winther, Ragnar
  email: rwinther@math.uio.no
  organization: Department of Mathematics, University of Oslo, Blindern, Oslo, 0316, Norway
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Snippet We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we...
We discuss the construction of robust preconditioners for finite element approximations of Biot’s consolidation model in poroelasticity. More precisely, we...
We discuss the construction of robust preconditioners for finite element approximationsof Biot’s consolidation model in poroelasticity. More precisely, we...
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walterdegruyter
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StartPage 377
SubjectTerms 65N30
65N55
74S05
Computational fluid dynamics
Conditioning
Consolidation
Discretization
Elasticity
Finite element method
Finite Elements
Mathematical models
Parameters
Poroelasticity
Preconditioning
Robustness
Tensors
Title Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model
URI https://www.degruyter.com/doi/10.1515/cmam-2017-0016
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Volume 17
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