A. Cangiani
hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems
Cangiani, A.; Georgoulis, E.H.; Giani, S.; Metcalfe, S.
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.
Citation
Cangiani, A., Georgoulis, E., Giani, S., & Metcalfe, S. (2019). hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. Computers and Mathematics with Applications, 78(9), 3090-3104. https://doi.org/10.1016/j.camwa.2019.04.002
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 5, 2019 |
Online Publication Date | May 13, 2019 |
Publication Date | Nov 1, 2019 |
Deposit Date | Apr 5, 2019 |
Publicly Available Date | Nov 13, 2020 |
Journal | Computers and Mathematics with Applications |
Print ISSN | 0898-1221 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 78 |
Issue | 9 |
Pages | 3090-3104 |
DOI | https://doi.org/10.1016/j.camwa.2019.04.002 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright 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/
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