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

Titlehp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems
Publication TypeJournal Article
Year of Publication2019
AuthorsCangiani, A, Georgoulis, EH, Giani, S, Metcalfe, S
JournalComputers & Mathematics with Applications
Volume78
Pagination3090-3104
ISSN0898-1221
KeywordsA posteriori error estimation; Adaptive finite element methods; Anisotropic meshes; Discontinuous Galerkin; Unsteady convection–diffusion
Abstract

An a posteriori error estimator for the error in the (L2(H1)+L∞(L2))-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.

URLhttps://www.sciencedirect.com/science/article/pii/S0898122119302007
DOI10.1016/j.camwa.2019.04.002

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