Stabilized Finite Element Methods for Biot's Consolidation Problems Using Equal Order Elements (Advances in Applied Mathematics and Mechanics, 2018)
Using the standard mixed Galerkin methods with equal order elements tosolve Biot's consolidation problems, the pressure close to the initial time produceslarge non-physical oscillations. In this paper, we propose a class of fully discrete stabilizedmethods using equal order elements to reduce the effects of non-physical oscillations.Optimal error estimates for the approximation of displacements and pressure atevery time level are obtained, which are valid even close to the initial time. Numericalexperiments illustrate and confirm our theoretical analysis.