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

Cangiani, A.; Georgoulis, E.H.; Giani, S.; Metcalfe, S.

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Authors

A. Cangiani

E.H. Georgoulis

S. Metcalfe



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 Mar 29, 2024
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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