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

Lorenzo Botti (1) , Michele Botti (2) , Daniele Antonio Di Pietro (3)

1 Department of Industrial Engineering
2 Dipartimento di Matematica "Francesco Brioschi" - Laboratorio di Modellistica e Calcolo Scientifico MOX
3 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Poroelasticity; Biot problem; Hybrid High-Order methods; polyhedral meshes; abstract analysis framework

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Lorenzo Botti, Michele Botti, Daniele Antonio Di Pietro. An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods. Computers & Mathematics with Applications, 2021, 91, pp.150-175. ⟨10.1016/j.camwa.2020.06.004⟩. ⟨hal-02398946⟩