A posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

Abstract

We develop a residual-based a posteriori error analysis for the augmented mixed methods introduced in [13] and [14] for the problem of linear elasticity in the plane. We prove that the proposed a posteriori error estimators are both reliable and efficient. Numerical experiments confirm these theoretical properties and illustrate the ability of the corresponding adaptive algorithms to localize the singularities and large stress regions of the solutions.