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A high-order discretization of nonlinear poroelasticity


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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Dates and versions

hal-01785810 , version 1 (04-05-2018)
hal-01785810 , version 2 (03-06-2019)


  • HAL Id : hal-01785810 , version 2


Michele Botti, Daniele Antonio Di Pietro, Pierre Sochala. A high-order discretization of nonlinear poroelasticity. 2019. ⟨hal-01785810v2⟩
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