منابع مشابه
Discrete Solution of the Plateau Problem and Its Convergence
In this paper we define a discrete solution of the Plateau problem and we prove theorems for the convergence of the discrete solution when the contour satisfies a certain condition. A numerical example is given.
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15 صفحه اولSolution of the Problem of Plateau*
ion being made, in case the representation g is improper of the first kind, of the values of 0, at most denumerably infinite in number, where gi(8) is discontinuous. (19.9) rests on the fact (whose proof is trivial) that if fiim)(l) tends uniformly to the continuous f((t) when m—>, then if tm—H as m—>«>, we have lim/i(m)(í„) =/i(i) for m—>°o. The assertion is now easily proved that if (19.10...
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The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. We establish the existence of an equilibrium shape that minimizes the total energy of the system under the ph...
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We solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating minimal, including unstable, surfaces. In a previous paper we introduced the general framework and some preliminary estimates, developed the algorithm and give the numerical results. In this paper we prove the convergence estimate.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1992
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.89.19.9235