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Title: $hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes
Authors: Cangiani, Andrea
Dong, Zhaonan
Georgoulis, Emmanuil H.
First Published: 4-May-2016
Publisher: Society for Industrial and Applied Mathematics
Citation: SIAM Journal on Scientific Computing, 2017, 39(4), A1251–A1279
Abstract: We present a new hp-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements, giving rise to prismatic space-time elements. A key feature of the proposed method is the use of space-time elemental polynomial bases of total degree, say p, defined in the physical coordinate system, as opposed to standard dG-time-stepping methods whereby spatial elemental bases are tensorized with temporal basis functions. This approach leads to a fully discrete hp-dG scheme using fewer degrees of freedom for each time step, compared to dG time-stepping schemes employing tensorized space-time basis, with acceptable deterioration of the approximation properties. A second key feature of the new space-time dG method is the incorporation of very general spatial meshes consisting of possibly polygonal/polyhedral elements with arbitrary number of faces. A priori error bounds are shown for the proposed method in various norms. An extensive comparison among the new space-time dG method, the (standard) tensorized space-time dG methods, the classical dG-time-stepping, and conforming finite element method in space, is presented in a series of numerical experiments.
DOI Link: 10.1137/16M1073285
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s open access archiving policy.
Description: AMS subject classifications. 65N30, 65M60, 65J10
Appears in Collections:Published Articles, Dept. of Mathematics

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