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

作者：Giani Stefano; Schoetzau Dominik; Zhu Liang

来源：Computers & Mathematics with Applications, 2014, 67(4): 869-887.

DOI：10.1016/j.camwa.2012.10.015

• Discontinuous Galerkin methods
• Error estimation
• hp-adaptivity
• Convection diffusion problems

We prove an a-posteriori error estimate for hp-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 hp-adaptive refinement algorithm.

• 出版日期2014-3