A nonconforming high-order method for the Biot problem on general meshes

Daniele Boffi (1) , Michele Botti (2, 1) , Daniele Antonio Di Pietro (2)

1 UNIPV - Università degli Studi di Pavia = University of Pavia
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

In this work, we introduce a novel algorithm for the Biot problem based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discretization of the flow. The method has several assets, including, in particular, the support of general polyhedral meshes and arbitrary space approximation order. Our analysis delivers stability and error estimates that hold also when the specific storage coefficient vanishes, and shows that the constants have only a mild dependence on the heterogeneity of the permeability coefficient. Numerical tests demonstrating the performance of the method are provided.

Domaines: Analyse numérique [math.NA]

Daniele Boffi, Michele Botti, Daniele Antonio Di Pietro. A nonconforming high-order method for the Biot problem on general meshes. 2015. ⟨hal-01162976v1⟩