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

TL;DR

This paper presents a new high-order, nonconforming numerical method for solving the Biot problem, capable of handling complex meshes and variable material properties with proven stability and accuracy.

Contribution

It introduces a hybrid high-order discretization combined with a symmetric interior penalty flow discretization, supporting general meshes and arbitrary approximation orders.

Findings

Method supports general polyhedral meshes.

Stability and error estimates are robust even when specific storage coefficient vanishes.

Numerical tests confirm the method's effectiveness.

Abstract

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.