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Finite element methods for surface PDEs
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Dziuk, Gerhard and Elliott, Charles M. (2013) Finite element methods for surface PDEs. Acta Numerica, Volume 22 . pp. 289-396. doi:10.1017/S0962492913000056 ISSN 0962-4929.
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Official URL: http://dx.doi.org/10.1017/S0962492913000056
Abstract
In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with illustrative numerical examples.
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, Differential equations, Partial, Hypersurfaces | ||||
Journal or Publication Title: | Acta Numerica | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0962-4929 | ||||
Official Date: | May 2013 | ||||
Dates: |
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Volume: | Volume 22 | ||||
Page Range: | pp. 289-396 | ||||
DOI: | 10.1017/S0962492913000056 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 24 December 2015 | ||||
Date of first compliant Open Access: | 24 December 2015 | ||||
Funder: | Deutsche Forschungsgemeinschaft (DFG) |
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