Plateau's problem for minimal surfaces with a catenoidal end

1992 ◽  
Vol 59 (2) ◽  
pp. 165-172 ◽  
Author(s):  
Friedrich Tomi
Keyword(s):  
Minimal Surfaces ◽  
Plateau’S Problem ◽  
Plateau's Problem

scholarly journals On solving the plateau problem in parametric form

1983 ◽  
Vol 6 (2) ◽  
pp. 341-361
Author(s):  
Baruch cahlon ◽  
Alan D. Solomon ◽  
Louis J. Nachman
Keyword(s):  
Minimal Surface ◽  
Numerical Method ◽  
Minimal Surfaces ◽  
Plateau Problem ◽  
Parametric Form ◽  
First Variation ◽  
Plateau’S Problem ◽  
Numerical Example ◽  
Plateau's Problem ◽  
The First Variation

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.

Numerical simulation of Plateau’s problem of minimal surfaces using nonvariational finite element method

2016 ◽  
Vol 33 (5) ◽  
pp. 1490-1507 ◽  
Author(s):  
Garima Mishra ◽  
Manoj Kumar
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Minimal Surfaces ◽  
Design Methodology ◽  
Engineering Application ◽  
Content Type ◽  
Plateau’S Problem ◽  
Plateau's Problem ◽  
Element Method

Purpose – Numerical solution of Plateau’s problem of minimal surface using non-variational finite element method. The paper aims to discuss this issue. Design/methodology/approach – An efficient algorithm is proposed for the computation of minimal surfaces and numerical results are presented. Findings – The solutions obtained here are examined for different cases of non-linearity and are found sufficiently accurate. Originality/value – The manuscript provide the non-variational solution for Plateau’s problem. Thus it has a good value in engineering application.

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