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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
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.

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Article copyright: © Copyright 1975 American Mathematical Society

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