Engwer, C, Ranner, T orcid.org/0000-0001-7682-3175 and Westerheide, S (2016) An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces. In: Handlovičová, A and Ševčovič,, D, (eds.) Proceedings of the Conference ALGORITMY 2016. ALGORITMY 2016, 14-18 Mar 2016, Podbanske, Slovakia. Publishing House of Slovak University of Technology in Bratislava ISBN 978-80-227-4544-4
Abstract
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on an unfitted discontinuous Galerkin approach where the surface is not explicitly tracked by the mesh which means the method is extremely flexible with respect to geometry. Furthermore, the discontinuous Galerkin approach is well-suited to capture the advection driven by the evolution of the surface without the need for a space-time formulation, back-tracking trajectories or streamline diffusion. The method is illustrated by a one-dimensional example and numerical results are presented that show good convergence properties for a simple test problem.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Keywords: | math.NA; 35L02, 35L65, 35Q90, 35R01, 65N12, 65N30 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Artificial Intelligence & Biological Systems (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Jun 2016 12:18 |
Last Modified: | 24 Jan 2018 09:57 |
Published Version: | http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/al... |
Status: | Published |
Publisher: | Publishing House of Slovak University of Technology in Bratislava |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:99578 |