New a Posteriori Error Estimator for an Augmented Mixed FEM in Linear Elasticity

Abstract

We consider an augmented mixed finite element method applied to the linear elasticity problem with non-homogeneous Dirichlet boundary conditions and derive an a posteriori error estimator that is simpler and easier to implement than the one available in the literature. The new a posteriori error estimator is reliable and locally efficient in interior triangles; in the remaining elements, it satisfies a quasi-efficiency bound. We provide some numerical results that illustrate the performance of the corresponding adaptive algorithm.