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

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.