A Posteriori Error Analysis of an Augmented Dual-Mixed Method in Linear Elasticity with Mixed Boundary Conditions

Abstract

We consider an augmented mixed finite element method for the equations of plane\r linear elasticity with mixed boundary conditions. The method provides simultaneous approximations of the displacements, the stress tensor and the rotation. We develop an a posteriori error\r analysis based on the Ritz projection of the error and the use of an appropriate auxiliary function, and derive fully local reliable a posteriori error estimates that are locally efficient up to the\r elements that touch the Neumann boundary. We provide numerical experiments that illustrate\r the performance of the corresponding adaptive algorithm and support its use in practice.