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.
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
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.