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