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An ALE ESFEM for solving PDEs on evolving surfaces
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Elliott, Charles M. and Styles, Vanessa (2012) An ALE ESFEM for solving PDEs on evolving surfaces. Milan Journal of Mathematics, Volume 80 (Number 2). pp. 469-501. doi:10.1007/s00032-012-0195-6 ISSN 1424-9286.
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Official URL: http://dx.doi.org/10.1007/s00032-012-0195-6
Abstract
Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented. In the ALE ESFEM the vertices of the triangles evolve with a velocity which is normal to the hypersurface whilst having a tangential velocity which is arbitrary. This is in contrast to the original evolving surface finite element method in which the nodes move with a material velocity. Numerical experiments are presented which illustrate the value of choosing the arbitrary tangential velocity to improve mesh quality. Simulations of two applications arising in material science and biology are presented which couple the evolution of the surface to the solution of the surface partial differential equation. © 2012 Springer Basel.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Finite element method, Heat equation, Differential equations, Partial, Hypersurfaces | ||||
Journal or Publication Title: | Milan Journal of Mathematics | ||||
Publisher: | Birkhaeuser Verlag AG | ||||
ISSN: | 1424-9286 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 80 | ||||
Number: | Number 2 | ||||
Page Range: | pp. 469-501 | ||||
DOI: | 10.1007/s00032-012-0195-6 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 23 December 2015 | ||||
Date of first compliant Open Access: | 23 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/D078334/1 (EPSRC), EP/G010404 (EPSRC) |
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