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

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posted on 2023-06-09, 12:16 authored by Emmanuil H Georgoulis, Edward Hall, Charalambos MakridakisCharalambos 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

Publication status

  • Published

File Version

  • Accepted version

Journal

IMA Journal of Numerical Analysis

ISSN

0272-4979

Publisher

Oxford University Press

Issue

1

Volume

39

Page range

34-60

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-20

First Open Access (FOA) Date

2018-12-22

First Compliant Deposit (FCD) Date

2018-02-20

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