An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity

We develop the a posteriori error estimation of mixed hp-version discontinuous Galerkin finite element methods for nearly incompressible elasticity problems in two space dimensions. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders, and are independent of the locking parameter. A series of numerical experiments are presented which demonstrate the performance of the proposed error estimator within an automatic hp-adaptive refinement procedure.