conv_diff_apost4_mm_V2 .pdf (350.3 kB)
Download file

An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems

Download (350.3 kB)
journal contribution
posted on 26.11.2020, 16:27 by Emmanuil H Georgoulis, Edward Hall, Charalambos Makridakis
An a posteriori bound for the error measured in the discontinuous energy norm for a discontinuous Galerkin (dG) discretization of a linear one-dimensional stationary convection-diffusion-reaction problem with essential boundary conditions is presented. The proof is based on a conforming recovery operator inspired from a posteriori error bounds for the dG method for first-order hyperbolic problems. As such, the bound remains valid in the singular limit of vanishing diffusion. Detailed numerical experiments demonstrate the independence of the quality of the a posteriori bound with respect to the Péclet number in the standard dG-energy norm, as well as with respect to the viscosity parameter.

History

Citation

IMA Journal of Numerical Analysis, Volume 39, Issue 1, January 2019, Pages 34–60, https://doi.org/10.1093/imanum/drx065

Author affiliation

School of Mathematics & Actuarial Science

Version

AM (Accepted Manuscript)

Published in

IMA Journal of Numerical Analysis

Volume

39

Issue

1

Pagination

34 - 60

Publisher

Oxford University Press (OUP) for Institute of Mathematics and its Applications

issn

0272-4979

eissn

1464-3642

Copyright date

2020

Available date

26/11/2020

Language

English