A nonconforming high-order method for nonlinear poroelasticity

Michele Botti (1) , Daniele Di Pietro (1) , Pierre Sochala (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

In this work, we introduce a novel algorithm for the quasi-static nonlin-ear poroelasticity problem describing Darcian flow in a deformable saturated porous medium. The nonlinear elasticity operator is discretized using a Hybrid High-Order method while the heterogeneous diffusion part 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, allows 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 rough variations of the permeability coefficient and vanishing specific storage coefficient. Numerical tests demonstrating the performance of the method are provided.

Mots clés: Nonlinear poroelasticity; Hybrid High-Order; discontinuous Galerkin; General meshes

Domaines: Analyse numérique [math.NA]

Michele Botti, Daniele Di Pietro, Pierre Sochala. A nonconforming high-order method for nonlinear poroelasticity. Finite volumes for complex applications VIII—hyperbolic, elliptic and parabolic problems, Jun 2017, Lille, France. pp.537-545, ⟨10.1007/978-3-319-57394-6_56⟩. ⟨hal-01439165v2⟩