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hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Andrea Cangiani

Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK

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Emmanuil H. Georgoulis

Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK

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and

Paul Houston

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

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https://doi.org/10.1142/S0218202514500146Cited by:119

Abstract

An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analyzed. Utilizing a bounding box concept, the method employs elemental polynomial bases of total degree p (𝒫_p-basis) defined on the physical space, without the need to map from a given reference or canonical frame. This, together with a new specific choice of the interior penalty parameter which allows for face-degeneration, ensures that optimal a priori bounds may be established, for general meshes including polygonal elements with degenerating edges in two dimensions and polyhedral elements with degenerating faces and/or edges in three dimensions. Numerical experiments highlighting the performance of the proposed method are presented. Moreover, the competitiveness of the p-version DGFEM employing a 𝒫_p-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem.

Keywords:

AMSC: 65N30, 65N50, 65N55

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Vol. 24, No. 10

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History

Received 11 July 2013

Revised 2 December 2013

Accepted 10 December 2013

Published: 11 March 2014

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hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Abstract

References

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