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|Title:||hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes|
Georgoulis, Emmanuil H.
|Publisher:||World Scientific Publishing|
|Citation:||Mathematical Models and Methods in Applied Sciences, 2014, 24 (10) pp. 2009-2041|
|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[subscript 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[subscript p]-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem.|
|Rights:||Copyright © 2014, World Scientific Publishing. Deposited with reference to the publisher’s open access archiving policy.|
|Description:||Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 24 (10), 2014, DOI:10.1142/S0218202514500146 © copyright World Scientific Publishing Company http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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