Error estimates for the web-Spline method

Authors:
Klaus Höllig;Ulrich Reif;Joachim Wipper
Affiliations:
Univ. Stuttgart, Stuttgart, Germany;TU Darmstadt, Darmstadt, Germany;Univ. Stuttgart, Stuttgart, Germany
Venue:
Mathematical Methods for Curves and Surfaces
Year:
2001

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Abstract

The web-spline method is a new finite element technique for solving elliptic boundary value problems on bounded domains in IRm. It is based on weighted extended B-splines and provides high accuracy approximations with relatively low dimensional subspaces. Further, it does not require any non-trivial grid generation process. In this paper, we review the method, prove stability, and present a Jackson-type error estimate showing that web-splines have optimal approximation order.