Seminars

Title: Dimension of C^1 splines in the plane

Abstract:

Given a triangulated polygon Π in R^2 , we consider the space of C^1 piecewise
polynomial functions of degree n defined in Π. We wish to study two questions:
what is the dimension of this space and what is a convenient basis for it. These
two questions were consider by Gilbert Strang and he conjectured a formula for
the dimension. In this talk I shall present some methods that have been used
to calculate the dimension, such as a recent application of the theory of Gröbner
basis and the method used by Morgan and Scott to construct a nodal basis which
verify the conjecture for most of the values of n. For the values of n for which
these are still open questions I will show some positive examples and one example
for n=2 where the formula does not give the correct dimension.