International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3291-3302
doi:10.1155/IJMMS.2005.3291
On Wk,p-manifolds and Wk,p-surfaces for analysis of the convergence of mesh-based approximation
The Aerospace Corporation, M4-960, P.O. Box 92957, Los Angeles 90009–2957, CA, USA
Received 3 January 2005; Revised 23 May 2005
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
To categorize the convergence properties of mesh-based approximations to manifolds and surfaces, this paper defines these approximations as “Wk,p-manifolds” and “Wk,p-surfaces.” In particular, this paper examines the importance of these classifications in the convergence in L1-norm of interpolants, built on the approximate manifold or surface, of functions defined on the approximated manifold or surface. To provide context, the applicability of an interpolation framework established by Nédélec involving the convergence of metric determinants is examined. An extension of Nédélec's framework to Wk,p-surfaces is presented.