hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes

Cangiani, Andrea and Dong, Zhaonan and Georgoulis, Emmanuil H. and Houston, Paul (2016) hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (3). pp. 699-725. ISSN 0764-583X

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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) Q_p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes.

Item Type: Article
Additional Information: Copyright EDP Sciences, SMAI 2016
Keywords: discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; P-basis; PDEs with nonnegative characteristic form
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1051/m2an/2015059
Depositing User: Houston, Paul
Date Deposited: 28 Aug 2015 07:30
Last Modified: 13 Sep 2016 19:42
URI: http://eprints.nottingham.ac.uk/id/eprint/29675

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