Discrete solution of the Plateau problem and its convergence

Author:
Takuya Tsuchiya

Journal:
Math. Comp. **49** (1987), 157-165

MSC:
Primary 49F10; Secondary 49D15

MathSciNet review:
890259

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

**[1]**Philippe G. Ciarlet,*Discrete maximum principle for finite-difference operators*, Aequationes Math.**4**(1970), 338–352. MR**0292317****[2]**Philippe G. Ciarlet,*The finite element method for elliptic problems*, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. Studies in Mathematics and its Applications, Vol. 4. MR**0520174****[3]**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****[4]**R. Courant,*Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces*, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. MR**0036317****[5]**R. Courant and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[6]**H. Blaine Lawson Jr.,*Lectures on minimal submanifolds. Vol. I*, 2nd ed., Mathematics Lecture Series, vol. 9, Publish or Perish, Inc., Wilmington, Del., 1980. MR**576752****[7]**Johannes C. C. Nitsche,*The boundary behavior of minimal surfaces. Kellogg’s theorem and Branch points on the boundary*, Invent. Math.**8**(1969), 313–333. MR**0259766****[8]**Robert Osserman,*A survey of minimal surfaces*, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR**0256278****[9]**Takuya Tsuchiya,*On two methods for approximating minimal surfaces in parametric form*, Math. Comp.**46**(1986), no. 174, 517–529. MR**829622**, 10.1090/S0025-5718-1986-0829622-1**[10]**Walter L. Wilson Jr.,*On discrete Dirichlet and Plateau problems*, Numer. Math.**3**(1961), 359–373. MR**0137309**

Retrieve articles in *Mathematics of Computation*
with MSC:
49F10,
49D15

Retrieve articles in all journals with MSC: 49F10, 49D15

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1987-0890259-0

Article copyright:
© Copyright 1987
American Mathematical Society