A finite element method with strong mass conservation for Biot's linear consolidation model

TL;DR

This paper introduces a finite element method that ensures strong mass conservation for Biot's linear consolidation model, combining mixed and discontinuous Galerkin formulations to achieve optimal convergence.

Contribution

It presents a novel finite element scheme that combines mixed and interior penalty discontinuous Galerkin methods for improved mass conservation in Biot's model.

Findings

Optimal convergence rates achieved

Method ensures strong mass conservation

Combines mixed and DG formulations effectively

Abstract

An H(div) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior penalty discontinuous Galerkin method to obtain a consistent scheme. Optimal convergence rates are obtained.