Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements

Abstract

Using the standard mixed Galerkin methods with equal order elements to solve Biot's consolidation problems, the pressure close to the initial time produces large non-physical oscillations. In this paper, we propose a class of fully discrete stabilized methods using equal order elements to reduce the effects of non-physical oscillations. Optimal error estimates for the approximation of displacements and pressure at every time level are obtained, which are valid even close to the initial time. Numerical experiments illustrate and confirm our theoretical analysis.