Finite element method with the total stress variable for Biot's consolidation model

TL;DR

This paper develops and validates finite element methods for Biot's consolidation model using a three-field formulation, providing error estimates and confirming convergence through computational experiments.

Contribution

It introduces semi-discrete and fully-discrete error estimates for a three-field finite element formulation of Biot's model, including total stress, with validation through benchmark tests.

Findings

Error estimates for the finite element scheme are derived.

Convergence orders are verified for lowest order finite elements.

The method is validated with benchmark examples.

Abstract

In this work, semi-discrete and fully-discrete error estimates are derived for the Biot's consolidation model described using a three-field finite element formulation. The fields include displacements, total stress and pressure. The model is implemented using a backward Euler discretization in time for the fully-discrete scheme and validated for benchmark examples. Computational experiments presented verifies the convergence orders for the lowest order finite elements with discontinuous and continuous finite element appropriation for the total stress.