An optimal-order L2-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions

Kaixin Wang, Hong Wang, Shuyu Sun*, Mary F. Wheeler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We analyze the nonsymmetric discontinuous Galerkin methods (NIPG and IIPG) for linear elliptic and parabolic equations with a spatially varied coefficient in multiple spatial dimensions. We consider d-linear approximation spaces on a uniform rectangular mesh, but our results can be extended to smoothly varying rectangular meshes. Using a blending or Boolean interpolation, we obtain a superconvergence error estimate in a discrete energy norm and an optimal-order error estimate in a semi-discrete norm for the parabolic equation. The L2-optimality for the elliptic problem follows directly from the parabolic estimates. Numerical results are provided to validate our theoretical estimates. We also discuss the impact of penalty parameters on convergence behaviors of NIPG.

Original languageEnglish (US)
Pages (from-to)2190-2197
Number of pages8
JournalComputer Methods in Applied Mechanics and Engineering
Volume198
Issue number27-29
DOIs
StatePublished - May 15 2009
Externally publishedYes

Keywords

  • Convergence analysis
  • Discontinuous Galerkin methods
  • Error estimates
  • IIPG
  • NIPG
  • Superconvergence

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint Dive into the research topics of 'An optimal-order L<sup>2</sup>-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions'. Together they form a unique fingerprint.

Cite this