Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 46, Issue 3, Pages 1250-1265Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060677215
Keywords
discontinuous Galerkin methods; transport; reaction equation; error estimates
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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 required only 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.
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