A posteriori error estimates for Biot system using a mixed discretization for flow

Abstract

We first derive convergence and a priori stability, and next reliability and efficiency of a posteriori error indicators for a Biot poroelastic model coupled with an elastic model in R3, solved by a continuous Galerkin scheme (CG) for the displacement and a mixed finite element scheme for the flow. The coupled system is decoupled by a fixed stress splitting algorithm. The numerical implementation of the residual based error indicators is simple, even for the mixed discretization, but at the expense of two suboptimal bounds. The scheme is tested on two benchmark problems via several numerical experiments.