Finite element approximation of 𝐻-surfaces

Matsuzawa, Yuki; Suzuki, Takashi; Tsuchiya, Takuya

doi:10.1090/S0025-5718-02-01447-3

Finite element approximation of $H$-surfaces
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by Yuki Matsuzawa, Takashi Suzuki and Takuya Tsuchiya;

Math. Comp. 72 (2003), 607-617

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

Published electronically: October 22, 2002

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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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Finite element approximation of $H$-surfaces
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Abstract: