Finite element approximation of -surfaces

Authors:
Yuki Matsuzawa, Takashi Suzuki and Takuya Tsuchiya

Journal:
Math. Comp. **72** (2003), 607-617

MSC (2000):
Primary 65N30, 35J65

DOI:
https://doi.org/10.1090/S0025-5718-02-01447-3

Published electronically:
October 22, 2002

MathSciNet review:
1954958

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a piecewise linear finite element approximation of -surfaces, or surfaces with constant mean curvature, spanned by a given Jordan curve in is considered. It is proved that the finite element -surfaces converge to the exact -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

Email:
suzuki@sigmath.es.osaka-u.ac.jp

**Takuya Tsuchiya**

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

Email:
tsuchiya@math.sci.ehime-u.ac.jp

DOI:
https://doi.org/10.1090/S0025-5718-02-01447-3

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