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Finite element methods for surface PDEs*

Published online by Cambridge University Press:  02 April 2013

Gerhard Dziuk  and
Charles M. Elliott
Gerhard Dziuk
Affiliation:
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg im Breisgau, Hermann-Herder-Straβe 10, D–79104 Freiburg im Breisgau, Germany E-mail: [email protected]
Charles M. Elliott
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK E-mail: [email protected]
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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.

Type
Research Article
Information
Acta Numerica , Volume 22 , May 2013 , pp. 289 - 396
Copyright
Copyright © Cambridge University Press 2013

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Footnotes

*

Colour online for monochrome figures available at journals.cambridge.org/anu.

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