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

Georgoulis, Emmanuil H, Hall, Edward and Makridakis, Charalambos (2017) An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA Journal of Numerical Analysis. ISSN 0272-4979

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 20 Feb 2018 13:53
Last Modified: 20 Feb 2018 13:53
URI: http://sro.sussex.ac.uk/id/eprint/73728

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