Local Flux Reconstruction for a Frictionless Unilateral Contact Problem

Abstract

We are interested in the a posteriori error analysis based on locally reconstructed fluxes for the 2D Signorini problem. We start from a P ¹-conforming approximation where the contact condition is treated by means of a Nitsche method. We propose an extension of a general approach previously developed for the Laplace operator, allowing to obtain H(div)-conforming conservative fluxes by a local post-process. The reconstructed flux yields an a posteriori error indicator, which is completed by two additional terms taking into account the non-linear contact condition. We then prove the reliability of the indicator, without any additional assumption.