Galerkin methods, Elasticity, Numerical analysis, Matrices
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 ap- proximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.
Bramwell, Jamie; Demkowicz, Leszek; Gopalakrishnan, Jay; and Qiu, Weifeng, "A Locking-Free hp DPG Method for Linear Elasticity with Symmetric Stresses" (2012). Mathematics and Statistics Faculty Publications and Presentations. 35.