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Finite element approximation of $H$-surfaces

Authors: Yuki Matsuzawa, Takashi Suzuki and Takuya Tsuchiya
Journal: Math. Comp. 72 (2003), 607-617
MSC (2000): Primary 65N30, 35J65
Published electronically: October 22, 2002
MathSciNet review: 1954958
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Abstract: In this paper a piecewise linear finite element approximation of $H$-surfaces, or surfaces with constant mean curvature, spanned by a given Jordan curve in $\textbf{R}^3$ is considered. It is proved that the finite element $H$-surfaces converge to the exact $H$-surfaces under the condition that the Jordan curve is rectifiable. Several numerical examples are given.

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Additional Information

Takashi Suzuki
Affiliation: Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka 560-0043, Japan

Takuya Tsuchiya
Affiliation: Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama 790-8577, Japan

Keywords: Finite element method, constant mean curvature, $H$-surfaces.
Received by editor(s): July 10, 2000
Received by editor(s) in revised form: February 28, 2001
Published electronically: October 22, 2002
Article copyright: © Copyright 2002 American Mathematical Society