Optimal convergence of the original DG method for the transport-reaction equation on special meshes

Bernardo Cockburn, Bo Dong, Johnny Guzmán

Research output: Contribution to journalArticlepeer-review

56 Scopus citations

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 L2-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.

Original languageEnglish (US)
Pages (from-to)1250-1265
Number of pages16
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number3
DOIs
StatePublished - Nov 10 2008

Keywords

  • Discontinuous Galerkin methods
  • Error estimates
  • Transport-reaction equation

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