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Error estimates for a finite element approximation of a minimal surface


Authors: Claes Johnson and Vidar Thomée
Journal: Math. Comp. 29 (1975), 343-349
MSC: Primary 65N15
DOI: https://doi.org/10.1090/S0025-5718-1975-0400741-X
MathSciNet review: 0400741
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Abstract: A finite element approximation of the minimal surface problem for a strictly convex bounded plane domain $ \Omega $ is considered. The approximating functions are continuous and piecewise linear on a triangulation of $ \Omega $. Error estimates of the form $ O(h)$ in the $ {H^1}$ norm and $ O({h^2})$ in the $ {L_p}$-norm $ (p < 2)$ are proved, where h denotes the maximal side in the triangulation.


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

  • [1] S. AGMON, Lectures on Elliptic Boundary Value Problems, Van Nostrand Math. Studies, No. 2, Van Nostrand, Princeton, N. J., 1965. MR 31 #2504. MR 0178246 (31:2504)
  • [2] C. B. MORREY, JR., Multiple Integrals in the Calculus of Variations, Die Grundlehren der math. Wissenschaften, Band 130, Springer-Verlag, New York, 1966. MR 34 #2380. MR 0202511 (34:2380)
  • [3] J. NITSCHE, "Lineare Spline-Funktionen und die Methoden von Ritz fur elliptische Randwertprobleme," Arch. Rational Mech. Anal., v. 36, 1970, pp. 348-355. MR 40 #8250. MR 0255043 (40:8250)
  • [4] O. A. LADYŽENSKAYA (LADYZHENSKAJA) & N. N. URAL'CEVA (URAL'TSEVA), Linear and Quasilinear Equations, Academic Press, New York, 1968. MR 39 #5941.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0400741-X
Article copyright: © Copyright 1975 American Mathematical Society

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