An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods

TL;DR

This paper introduces a new abstract framework for analyzing the stability and convergence of coupled discretizations of poroelasticity problems, specifically applying it to Hybrid High-Order schemes with novel regularity results.

Contribution

The work presents a new abstract analysis framework for poroelasticity discretizations, including novel regularity results and a family of Hybrid High-Order schemes.

Findings

Framework based on mild regularity assumptions

New regularity results for the Biot problem

Numerical evaluation of HHO schemes

Abstract

In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an appropriate weak formulation of the continuous problem. To the best of our knowledge, these regularity results for the Biot problem are new. A novel family of HHO discretisation schemes is proposed and analysed, and their performance numerically evaluated.