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

Abstract

AbstractIn 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. These 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 are presented to verify the convergence orders for two finite elements with discontinuous and continuous approximations for the total stress.