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