Discrete solution of the Plateau problem and its convergence
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- by Takuya Tsuchiya PDF
- Math. Comp. 49 (1987), 157-165 Request permission
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.References
- Philippe G. Ciarlet, Discrete maximum principle for finite-difference operators, Aequationes Math. 4 (1970), 338–352. MR 292317, DOI 10.1007/BF01844166
- Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
- 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 375802, DOI 10.1016/0045-7825(73)90019-4
- R. Courant, Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. MR 0036317
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, Monografías de Matemática [Mathematical Monographs], vol. 14, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977. MR 527121
- 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 259766, DOI 10.1007/BF01404636
- Robert Osserman, A survey of minimal surfaces, Van Nostrand Reinhold Co., New York-London-Melbourne, 1969. MR 0256278
- Takuya Tsuchiya, On two methods for approximating minimal surfaces in parametric form, Math. Comp. 46 (1986), no. 174, 517–529. MR 829622, DOI 10.1090/S0025-5718-1986-0829622-1
- Walter L. Wilson Jr., On discrete Dirichlet and Plateau problems, Numer. Math. 3 (1961), 359–373. MR 137309, DOI 10.1007/BF01386035
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Math. Comp. 49 (1987), 157-165
- MSC: Primary 49F10; Secondary 49D15
- DOI: https://doi.org/10.1090/S0025-5718-1987-0890259-0
- MathSciNet review: 890259