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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1067-1083
http://dx.doi.org/10.1155/IJMMS.2005.1067

Mesh-based interpolation on 2-manifolds

The Aerospace Corporation, P.O. Box 92957, Los Angeles 90009-2957, CA, USA

Received 1 September 2004; Revised 20 December 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a global L1-estimate for the convergence of mesh-based interpolants on 2-manifolds defined over multiple coordinate systems and analyzes the convergence of an integral on a triangulated approximate manifold to the desired integral on the manifold being approximated. To place this estimate in context, previous convergence estimates for interpolation techniques on manifolds are presented. Finally, numerical results demonstrating the value of the L1-estimate are presented.