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hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems.

Cangiani, A. and Georgoulis, E. H. and Giani, S. and Metcalfe, S. (2019) 'hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems.', Computers and mathematics with applications., 78 (9). pp. 3090-3104.

Abstract

An a posteriori error estimator for the error in the (L2(H1)+L1(L2))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection-diusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space-time adaptive algorithm wherein directional mesh renement is employed to give rise to highly anisotropic elements able to accurately capture layers. The performance of the hp-space-time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.camwa.2019.04.002
Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:05 April 2019
Date deposited:05 April 2019
Date of first online publication:13 May 2019
Date first made open access:13 May 2020

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