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Characteristic cut finite element methods for convection-diffusion problems on time dependent surfaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-4911-467X
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. (C) 2015 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 293, 431-461 p.
Keyword [en]
Cut finite element method, Surfactants, PDEs on surfaces, Characteristic Galerkin method
National Category
Computational Mathematics Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-174938DOI: 10.1016/j.cma.2015.05.010ISI: 000361475900020Scopus ID: 2-s2.0-84935019131OAI: oai:DiVA.org:kth-174938DiVA: diva2:865236
Funder
Swedish Research Council
Note

QC 20151027

Available from: 2015-10-27 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approved

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Zahedi, Sara

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