Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEM in Nearly Incompressible Linear Elasticity

We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discussed. Numerical simulations show only moderate deterioration of the effectivity index for a Poisson ratio close to 1 2 . 2010 Mathematical subject classification: 65N15; 65N30; 65N50; 74B05; 74G15.