  We present two new methods for linear elasticity with simultaneously yield
stress and displacement approximations of optimal accuracy in both the mesh
size h and polynomial degree p. This is achieved within the recently developed
discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the
stress and the displacement approximations are discontinuous across element
interfaces. We study locking-free convergence properties and the
interrelationships between the two DPG methods.
