Improved accuracy in finite element analysis of Biot's consolidation problem

Abstract

Numerical analysis and error estimates of finite element approximations of Biot's consolidation problem are presented. Initially different orders of interpolation are employed, leading to lower orders of convergence for the pore pressure compared to the displacements of the porous medium. Lower accuracy also occurs in the approximation of the effective stress tensor, whether it is calculated directly from the constitutive equation, or through a primal mixed stress formulation. To improve the rates of convergence of the pore pressure and effective stresses, a sequential Galerkin Petrov-Galerkin post-processing technique is proposed.