Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A note on discrete solutions of the Plateau problem


Author: Takuya Tsuchiya
Journal: Math. Comp. 54 (1990), 131-138
MSC: Primary 49Q05; Secondary 65E05, 65N30
DOI: https://doi.org/10.1090/S0025-5718-1990-0993934-2
MathSciNet review: 993934
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove theorems for convergence of discrete solutions of the Plateau problem under the assumption that the contour is rectifiable.


References [Enhancements On Off] (What's this?)

  • [1] P. G. Ciarlet and P. A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg. 2 (1973), 17-31. MR 0375802 (51:11992)
  • [2] R. Courant, Dirichlet's principle, conformal mapping, and minimal surfaces, Interscience, New York, 1950. MR 0036317 (12:90a)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Interscience, New York, 1962. MR 0065391 (16:426a)
  • [4] H. B. Lawson, Jr., Lectures on minimal submanifolds, Vol. I, Publish or Perish, Berkeley, 1980. MR 576752 (82d:53035b)
  • [5] R. Osserman, A survey of minimal surfaces, 2nd ed., Dover, New York, 1986. MR 852409 (87j:53012)
  • [6] T. Tsuchiya, On two methods for approximating minimal surfaces in parametric form, Math. Comp. 46 (1986), 517-529. MR 829622 (87d:49043)
  • [7] -, Discrete solution of the Plateau problem and its convergence, Math. Comp. 49 (1987), 157-165. MR 890259 (88i:49032)
  • [8] W. L. Wilson, Jr., On discrete Dirkhlet and Plateau problems, Numer. Math. 3 (1961), 359-373. MR 0137309 (25:761)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 49Q05, 65E05, 65N30

Retrieve articles in all journals with MSC: 49Q05, 65E05, 65N30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-0993934-2
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society