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Numerical solution of Plateau's problem by a finite element method

Authors: Masahiro Hinata, Masaaki Shimasaki and Takeshi Kiyono
Journal: Math. Comp. 28 (1974), 45-60
MSC: Primary 65N35; Secondary 49F10
MathSciNet review: 0331819
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Abstract: This paper concerns the application of a finite element method to the numerical solution of a nonrestricted form of the Plateau problem, as well as to a free boundary problem of Plateau type. The solutions obtained here are examined for several examples and are considered to be sufficiently accurate.

It is also observed that the hysteresis effect, which is a feature of a nonlinear problem, appears in this problem.

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Keywords: A boundary-value problem, a finite element method, a free boundary problem, cylindrical coordinate system, R. Courant's example, the hysteresis effect of Plateau's problem
Article copyright: © Copyright 1974 American Mathematical Society

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