Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 0400741
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0178246 (31 #2504)
  • [2] Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511 (34 #2380)
  • [3] J. Nitsche, Lineare Spline-Funktionen und die Methoden von Ritz für elliptische Randwertprobleme, Arch. Rational Mech. Anal. 36 (1970), 348–355 (German). 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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N15

Retrieve articles in all journals with MSC: 65N15


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1975-0400741-X
PII: S 0025-5718(1975)0400741-X
Article copyright: © Copyright 1975 American Mathematical Society