A posteriori error estimate for contact problems in porous media

Abstract

We present a family of generic a posteriori error estimators for the two-field Biot contact problem. While every family member of these estimators is reliable only certain members are also efficient. A crucial property of our error estimator is that it can measure the error of any approximation, not only of approximations with Galerkin orthogonality. Hence, it can be easily coupled with primal-dual active set algorithms. Additionally, we present explicitly an hp-finite element discretization and its residual based a posteriori error estimator based on the generic setup. Several numerical experiments underline the theoretical results.