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Optimal BV estimates for a discontinuous Galerkin method for linear elasticity

Lew, Adrian and Neff, Patrizio and Sulsky, Deborah and Ortiz, Michael (2004) Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Applied Mathematics Research eXpress, 2004 (3). pp. 73-106. ISSN 1687-1200. doi:10.1155/S1687120004020052.

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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.

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Ortiz, Michael0000-0001-5877-4824
Additional Information:© 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.
Issue or Number:3
Record Number:CaltechAUTHORS:20110823-091200001
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24990
Deposited By: Tony Diaz
Deposited On:12 Sep 2011 15:41
Last Modified:09 Nov 2021 16:28

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