Cantin, P;
Bonelle, J;
Burman, E;
Ern, A;
(2016)
A vertex-based scheme on polyhedral meshes for advection–reaction equations with sub-mesh stabilization.
Computers & Mathematics with Applications
, 72
(9)
pp. 2057-2071.
10.1016/j.camwa.2016.07.038.
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Abstract
We devise and analyze vertex-based schemes on polyhedral meshes to approximate advection–reaction equations. Error estimates of order O(h3/2) are established in the discrete inf–sup stability norm which includes the mesh-dependent weighted advective derivative. The two key ingredients are a local polyhedral reconstruction map leaving affine polynomials invariant, and a local design of stabilization whereby gradient jumps are only penalized across some subfaces in the interior of each mesh cell. Numerical results are presented on three-dimensional polyhedral meshes.
| Type: | Article |
|---|---|
| Title: | A vertex-based scheme on polyhedral meshes for advection–reaction equations with sub-mesh stabilization |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.camwa.2016.07.038 |
| Publisher version: | http://doi.org/10.1016/j.camwa.2016.07.038 |
| Language: | English |
| Additional information: | © 2016 Elsevier Ltd. All rights reserved. This manuscript version is made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at http://creativecommons.org/ licenses/by/4.0. Access may be initially restricted by the publisher. |
| Keywords: | Vertex-based scheme; Polyhedral meshes; Advection–reaction problems; Static condensation |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1529827 |
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