Cangiani, Andrea, Dong, Zhaonan  ORCID: https://orcid.org/0000-0003-4083-6593 and Georgoulis, Emmanuil H.
2017.
$hp$-version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes.
SIAM Journal on Scientific Computing
39
(4)
, A1251-A1279.
10.1137/16M1073285
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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 a 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 an 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 the conforming finite element method in space is presented in a series of numerical experiments.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 1064-8275 |
| Date of First Compliant Deposit: | 16 December 2019 |
| Date of Acceptance: | 27 April 2017 |
| Last Modified: | 04 Dec 2024 22:00 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/127569 |
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