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On the Dimension of Multivariate Piecewise Polynomials Peter Alfeld

Summary: On the Dimension of Multivariate Piecewise Polynomials
Peter Alfeld
Department of Mathematics
University of Utah
Salt Lake City, Utah 84112
Note: A slightly different version of this paper is to appear in the Proceedings of the Biennial Dundee
Conference on Numerical Analysis, June 25­28, 1985, Pitman Publishers
Lower bounds are given on the dimension of piecewise polynomial C 1 and C 2 functions defined on a tes­
sellation of a polyhedral domain into Tetrahedra. The analysis technique consists of embedding the space
of interest into a larger space with a simpler structure, and then making appropriate adjustments. In the
bivariate case, this approach reproduces the well­known lower bounds derived by Schumaker.
Table of Contents
1. Introduction
2. The Univariate Case
3. The Bivariate Case
3.1 The Geometry of Triangulations
3.2 The C 1 Case
3.3 The C 2 Case


Source: Alfeld, Peter - Department of Mathematics, University of Utah


Collections: Mathematics