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OPTIMAL CONVERGENCE OF THE ORIGINAL DG METHOD FOR THE TRANSPORT-REACTION EQUATION ON SPECIAL MESHES

By Bernardo Cockburn, Bo Dong and Johnny Guzmán

Abstract

Abstract. We show that the approximation given by the original discontinuous Galerkin method for the transport-reaction equation in d space dimensions is optimal provided the meshes are suitably chosen: the L 2-norm of the error is of order k + 1 when the method uses polynomials of degree k. These meshes are not necessarily conforming and do not satisfy any uniformity condition; they are only required to be made of simplexes each of which has a unique outflow face. We also find a new, element-by-element postprocessing of the derivative in the direction of the flow which superconverges with order k + 1

Topics: Key words. discontinuous Galerkin methods, transport-reaction equation, error estimates
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.1457
Provided by: CiteSeerX
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