期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 24, 期 10, 页码 2009-2041出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202514500146
关键词
Discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; P-basis
资金
- Leverhulme Trust
- Engineering and Physical Sciences Research Council [1464919, EP/L022745/1] Funding Source: researchfish
- EPSRC [EP/L022745/1] Funding Source: UKRI
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.
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