A residual-based a posteriori error estimator for the plane linear elasticity problem with pure traction boundary conditions

In this work we consider the two-dimensional linear elasticity problem with pure non-homogeneous Neumann boundary conditions, and derive a reliable and efficient residual-based a posteriori error estimator for the corresponding stress–displacement–rotation dual-mixed variational formulation. The proof of reliability makes use of a suitable auxiliary problem, the continuous inf–sup conditions satisfied by the bilinear forms involved, and the local approximation properties of the Clément and Raviart–Thomas interpolation operators. In turn, inverse and discrete trace inequalities, and the localization technique based on triangle-bubble and edge-bubble functions, are the main tools yielding the efficiency of the estimator. Several numerical results confirming the properties of the estimator and illustrating the performance of the associated adaptive algorithm are also reported.