An a Posteriori Error Estimator for Two-Body Contact Problems on Non-Matching Meshes

Abstract

A posteriori error estimates for two-body contact problems are established. The discretization is based on mortar finite elements with dual Lagrange multipliers. To define locally the error estimator, Arnold---Winther elements for the stress and equilibrated fluxes for the surface traction are used. Using the Lagrange multiplier on the contact zone as Neumann boundary conditions, equilibrated fluxes can be locally computed. In terms of these fluxes, we define on each element a symmetric and globally H(div)-conforming approximation for the stress. Upper and lower bounds for the discretization error in the energy norm are provided. In contrast to many other approaches, the constant in the upper bound is, up to higher order terms, equal to one. Numerical examples illustrate the reliability and efficiency of the estimator.