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Characteristic cut finite element methods for convection–diffusion problems on time dependent surfaces
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization. Jönköping University, School of Engineering, JTH, Product Development.
Umeå University.
KTH Royal Institute of Technology.
2015 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 293, 431-461 p.Article in journal (Refereed) Published
Abstract [en]

We develop a finite element method for convection–diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant. The method is based on a characteristic-Galerkin formulation combined with a piecewise linear cut finite element method in space. The cut finite element method is constructed by embedding the surface in a background grid and then using the restriction to the surface of a finite element space defined on the background grid. The surface is allowed to cut through the background grid in an arbitrary fashion. To ensure stability and well posedness of the resulting algebraic systems of equations, independent of the position of the surface in the background grid, we add a consistent stabilization term. We prove error estimates and present confirming numerical results.

Place, publisher, year, edition, pages
2015. Vol. 293, 431-461 p.
Keyword [en]
Cut finite element method; Surfactants; PDEs on surfaces; Characteristic Galerkin method
National Category
Fluid Mechanics and Acoustics Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-26977DOI: 10.1016/j.cma.2015.05.010ISI: 000361475900020Scopus ID: 2-s2.0-84935019131OAI: oai:DiVA.org:hj-26977DiVA: diva2:817424
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708Swedish Research Council, 2014-4804Swedish e‐Science Research Center
Available from: 2015-06-05 Created: 2015-06-05 Last updated: 2016-10-20Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • vancouver
  • Other style
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  • de-DE
  • en-GB
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  • nn-NB
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Output format
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