Skip to main content

Research Repository

Advanced Search

An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes

Giani, Stefano; Schötzau, Dominik; Zhu, Liang

An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes Thumbnail


Authors

Dominik Schötzau

Liang Zhu



Abstract

We prove an a-posteriori error estimate for hphp-adaptive discontinuous Galerkin methods for the numerical solution of convection–diffusion equations on anisotropically refined rectangular elements. The estimate yields global upper and lower bounds of the errors measured in terms of a natural norm associated with diffusion and a semi-norm associated with convection. The anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure. We present a series of numerical experiments to test the feasibility of this approach within a fully automated hphp-adaptive refinement algorithm.

Citation

Giani, S., Schötzau, D., & Zhu, L. (2014). An a-posteriori error estimate for hp-adaptive DG methods for convection–diffusion problems on anisotropically refined meshes. Computers and Mathematics with Applications, 67(4), 869-887. https://doi.org/10.1016/j.camwa.2012.10.015

Journal Article Type Article
Publication Date Mar 1, 2014
Deposit Date Sep 29, 2014
Publicly Available Date Jun 22, 2015
Journal Computers and Mathematics with Applications
Print ISSN 0898-1221
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 67
Issue 4
Pages 869-887
DOI https://doi.org/10.1016/j.camwa.2012.10.015
Keywords Discontinuous Galerkin methods, Error estimation, hp-adaptivity, Convection–diffusion problems.
Public URL https://durham-repository.worktribe.com/output/1453536

Files

Accepted Journal Article (1.5 Mb)
PDF

Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Computers & Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, 67, 4, March 2014, 10.1016/j.camwa.2012.10.015.





You might also like



Downloadable Citations