Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis

Abstract

We present an a posteriori error estimate for the linear elasticity problem. The estimate is based on an equilibrated reconstruction of the Cauchy stress tensor, which is obtained from mixed finite element solutions of local Neumann problems. We propose two different reconstructions: one using Arnold–Winther mixed finite element spaces providing a symmetric stress tensor, and one using Arnold–Falk–Winther mixed finite element spaces with a weak symmetry constraint. The performance of the estimate is illustrated on a numerical test with analytical solution.