We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (P p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a P p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) P p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.

Hp -Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes / Cangiani, A.; Dong, Z.; Georgoulis, E. H.; Houston, P.. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 50:3(2016), pp. 699-725. [10.1051/m2an/2015059]

Hp -Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes

Cangiani A.;Dong Z.;
2016-01-01

Abstract

We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (P p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a P p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) P p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.
2016
50
3
699
725
Cangiani, A.; Dong, Z.; Georgoulis, E. H.; Houston, P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135247
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