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hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul

Authors

Andrea Cangiani Andrea.Cangiani@le.ac.uk

Emmanuil H. Georgoulis Emmanuil.Georgoulis@mcs.le.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk



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 analysed. 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.

Journal Article Type Article
Publication Date 2014-09
Journal Mathematical Models and Methods in Applied Sciences
Print ISSN 0218-2025
Electronic ISSN 0218-2025
Publisher World Scientific
Peer Reviewed Peer Reviewed
Volume 24
Issue 10
Pages 2009-2041
APA6 Citation Cangiani, A., Georgoulis, E. H., & Houston, P. (2014). hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 24(10), 2009-2041. doi:10.1142/S0218202514500146
DOI https://doi.org/10.1142/S0218202514500146
Keywords Discontinuous Galerkin, polygonal elements, polyhedral elements, hp-finite elements, inverse estimates, P-basis
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Electronic version of an article published in Mathematical Models and Methods, vol. 24, issue 10, 2014, p. 2009-2041, doi: 10.1142/S0218202514500146 ©World Scientific Publishing Company http://www.worldscientific.com/worldscinet/m3as

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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