A Weighted Least-Squares Finite Element Method for Biot’s Consolidation Problem

Abstract

This paper examines a weighted least-squares method for a poroelastic structure governed by Biot’s consolidation model. Quasi-static model equations are converted to a first-order system of four-field, and the least-squares functional is defined for the time discretized system. We consider two different sets of weights for the functional and show its coercivity and continuity properties, from which an a priori error estimate for the primal variables is derived. Numerical experiments are provided to illustrate the performance of the proposed method.