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.

hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems / Cangiani, A.; Georgoulis, E. H.; Giani, S.; Metcalfe, S.. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 78:9(2019), pp. 3090-3104. [10.1016/j.camwa.2019.04.002]

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

Cangiani A.;Giani S.
;
2019-01-01

Abstract

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.
2019
78
9
3090
3104
Cangiani, A.; Georgoulis, E. H.; Giani, S.; Metcalfe, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135242
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