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

Giani, Stefano; Schötzau, Dominik; Zhu, Liang

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.