A priori and a posteriori error estimates for hp-FEM for a Bingham type variational inequality of the second kind

A hp-finite element discretization of a Bingham type variational inequality of the second kind is being analyzed. We prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the discrete FE-solution. The friction functional may be regularized in which case we also prove convergence and convergence rates in the regularization parameter ϵ. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. The exact computable member of each family of a posteriori error estimators with minimal value is proven to satisfy an efficiency estimate. Numerical results underline the theoretical finding.