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

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journal contribution
posted on 24.07.2019, 13:38 by A. Cangiani, E. H. Georgoulis, S. Giani, S. Metcalfe
An a posteriori error estimator for the error in the (L 2 (H 1 )+L ∞ (L 2 ))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection–diffusion 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 refinement 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.

History

Citation

Computers and Mathematics with Applications, 2019

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Computers and Mathematics with Applications

Publisher

Elsevier

issn

0898-1221

Acceptance date

04/04/2019

Copyright date

2019

Publisher version

https://www.sciencedirect.com/science/article/pii/S0898122119302007?via=ihub

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en