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

Giani, Stefano; Schötzau, Dominik; Zhu, Liang

doi:10.1016/j.camwa.2012.10.015

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

Giani, Stefano; Schötzau, Dominik; Zhu, Liang

Authors

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

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.

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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.