IJPAM: Volume 69, No. 4 (2011)
THE THREE-DIMENSIONAL ELECTROSTATIC PROBLEM
Department of Mathematics
University of Cergy-Pontoise
AGM, CNRS, UMR 8088, 2 Avenue Adolphe Chauvin
Cergy-Pontoise Cedex, 95302, FRANCE
Abstract. In this paper a new discontinuous Galerkin method for the three dimensional electrostatic problem is presented. The divergence contraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the element interface are penalized. Optimal error estimates in a discrete energy norm are proved. Some numerical experiments confirm the theoretical predictions.
Received: August 1, 2009
AMS Subject Classification: 65N32
Key Words and Phrases: discontinuous Galerkin method, electrostatic problem
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395