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The Multivariate Spline Method for Scattered Data Fitting and Numerical Solutions
 

Summary: The Multivariate Spline Method for
Scattered Data Fitting and Numerical Solutions
of Partial Differential Equations
Gerard Awanou, Ming-Jun Lai and Paul Wenston
Dedicated to Charles K. Chui on the Occasion of his 65th Birthday
Abstract. Multivariate spline functions are smooth piecewise poly-
nomial functions over triangulations consisting of n-simplices in the
Euclidean space IRn
. A straightforward method for using these spline
functions to fit given scattered data and numerically solve elliptic par-
tial differential equations is presented . This method does not require
constructing macro-elements or locally supported basis functions nor
computing the dimension of the finite element spaces or spline spaces.
The method for splines in IR2
and IR3
has been implemented in MAT-
LAB. Several numerical examples are shown to demonstrate the effec-
tiveness and efficiency of the method.
Table of Contents
[0] Introduction

  

Source: Awanou, Gerard - Department of Mathematical Sciences, Northern Illinois University

 

Collections: Mathematics