Optimal convergence of the original DG method on special meshes for variable transport velocity

Bernardo Cockburn, Bo Dong, Johnny Guzmán, Jianliang Qian

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We prove optimal convergence rates for the approximation provided by the original discontinuous Galerkin method for the transport-reaction problem. This is achieved in any dimension on meshes related in a suitable way to the possibly variable velocity carrying out the transport. Thus, if the method uses polynomials of degree k, the L2-norm of the error is of order k + 1. Moreover, we also show that, by means of an element-by-element postprocessing, a new approximate flux can be obtained which superconverges with order k + 1.

Original languageEnglish (US)
Pages (from-to)133-146
Number of pages14
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number1
DOIs
StatePublished - May 10 2010

Keywords

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

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