Accurate Upper Bounds of the Error in the Finite Element Method Using an Equilibrated Moving Least Squares Recovery Technique

Abstract

International audienceIn this paper we present preliminary results of a novel technique developed to obtain upper bounds of the error in energy norm through a recovery technique based on a Moving Least Squares (MLS) approach. The continuity requirement is easily satisfied because of the MLS approximation properties. On the other hand static admissibility has been obtained using the Lagrange multipliers technique to impose the satisfaction of the equilibrium equations (both, in the interior of the domain and along the Newman boundaries) to the local polynomial approximation of the stresses