A Hybrid High-Order Discretization Method for Nonlinear Poroelasticity
| Autor: | Pierre Sochala, Michele Botti, Daniele Antonio Di Pietro |
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| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Discretization Korn's Inequality Applied Mathematics Poromechanics Nonlinear Poroelasticity 010103 numerical & computational mathematics 01 natural sciences Discontinuous Galerkin Methods 010101 applied mathematics Computational Mathematics Nonlinear system Hybrid High-Order Methods Nonlinear Biot Problem Polyhedral Meshes Korn's inequality Applied mathematics 0101 mathematics High order Mathematics |
| Zdroj: | Computational Methods in Applied Mathematics. 20:227-249 |
| ISSN: | 1609-9389 1609-4840 |
| DOI: | 10.1515/cmam-2018-0142 |
| Popis: | In this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients. |
| Databáze: | OpenAIRE |
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