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-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-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem. © World Scientific Publishing Company.

Hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes / Cangiani, A.; Georgoulis, E. H.; Houston, P.. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 24:10(2014), pp. 2009-2041. [10.1142/S0218202514500146]

Hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Cangiani A.;
2014-01-01

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-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-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem. © World Scientific Publishing Company.
2014
24
10
2009
2041
Cangiani, A.; 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/20.500.11767/135252
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