Abstract
We present two new methods for linear elasticity that 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.
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