Stability and a posteriori error analysis of discontinuous Galerkin methods for linearized elasticity

We consider discontinuous Galerkin finite element methods for the discretization of linearized elasticity problems in two space dimensions. Inf–sup stability results on the continuous and the discrete level are provided. Furthermore, we derive upper and lower a posteriori error bounds that are robust with respect to nearly incompressible materials, and can easily be implemented within an automatic mesh refinement procedure. The theoretical results are illustrated with a series of numerical experiments.