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. Download PDF (856Kb) |
| 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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