International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1067-1083
doi: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 Kevin Scully. 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.