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arXiv · 1906.00757

A high-order discretization of nonlinear poroelasticity

Michele Botti·Daniele A. Di Pietro·Pierre Sochala
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Abstract

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.

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Michele Botti, Daniele A. Di Pietro, Pierre Sochala. 2019-06-03. A high-order discretization of nonlinear poroelasticity. https://arxiv.org/abs/1906.00757

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