Weakly Imposed Symmetry and Robust Preconditioners for Biot’s Consolidation Model
| Autor: | Trygve Bærland, Jeonghun J. Lee, Ragnar Winther, Kent-Andre Mardal |
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| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Biot number Consolidation (soil) Discretization Cauchy stress tensor Applied Mathematics Poromechanics Linear elasticity 010103 numerical & computational mathematics 01 natural sciences Computer Science::Numerical Analysis Finite element method 3. Good health 010101 applied mathematics Computational Mathematics Classical mechanics Compressibility Applied mathematics 0101 mathematics Mathematics |
| ISSN: | 1609-4840 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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