Optimal BV estimates for a discontinuous Galerkin method for linear elasticity
We analyze a discontinuous Galerkin method for linear elasticity. The discrete formulation derives from the Hellinger-Reissner variational principle with the addition of stabilization terms analogous to those previously considered by others for the Navier-Stokes equations and a scalar Poisson equation. For our formulation, we first obtain convergence in a mesh-dependent norm and in the natural mesh-independent BD norm. We then prove a generalization of Korn's second inequality which allows us to strengthen our results to an optimal, mesh-independent BV estimate for the error.
© 2004 Hindawi Publishing Corporation. Received February 2, 2004. Accepted July 29, 2004. Communicated by Thomas Yizhao Hou. Patrizio Neff and Deborah Sulsky acknowledge the kind hospitality of the Graduate Aeronautical Laboratories during their visits. We thank Donatella Marini, Ilaria Perugia, and Dominik Schötzau for comments on an earlier draft of this paper.