A high-order discretization of nonlinear poroelasticity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866909321088991232 |
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| author | Botti, Michele Di Pietro, Daniele A. Sochala, Pierre |
| author_facet | Botti, Michele Di Pietro, Daniele A. Sochala, Pierre |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_00757 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A high-order discretization of nonlinear poroelasticity Botti, Michele Di Pietro, Daniele A. Sochala, Pierre Numerical Analysis 65N08, 65N30, 76S05 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. |
| title | A high-order discretization of nonlinear poroelasticity |
| topic | Numerical Analysis 65N08, 65N30, 76S05 |
| url | https://arxiv.org/abs/1906.00757 |