 
Summary: On the Dimension of Multivariate Piecewise Polynomials
by
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
Abstract
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
