A nonconforming high-order method for the Biot problem on general meshes
Provides a robust, high-order numerical method for poroelasticity problems in geoscience and biomechanics, handling complex meshes and heterogeneous media.
The authors propose a new algorithm for the Biot problem combining Hybrid High-Order and Symmetric Weighted Interior Penalty discretizations, supporting general polyhedral meshes and arbitrary order. Stability and error estimates are proven even with vanishing storage coefficient, with constants mildly dependent on permeability heterogeneity.
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.