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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| Vydáno v: | Journal of computational methods in applied mathematics Ročník 17; číslo 3; s. 377 - 396 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Minsk
De Gruyter
01.07.2017
Walter de Gruyter GmbH |
| Témata: | |
| ISSN: | 1609-4840, 1609-9389 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1609-4840 1609-9389 |
| DOI: | 10.1515/cmam-2017-0016 |