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An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems
journal contribution
posted on 2023-06-09, 12:16 authored by Emmanuil H Georgoulis, Edward Hall, Charalambos MakridakisCharalambos MakridakisAn 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.
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Publication status
- Published
File Version
- Accepted version
Journal
IMA Journal of Numerical AnalysisISSN
0272-4979Publisher
Oxford University PressPublisher URL
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Issue
1Volume
39Page range
34-60Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-02-20First Open Access (FOA) Date
2018-12-22First Compliant Deposit (FCD) Date
2018-02-20Usage metrics
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