Bivariate Quadratic B-splines Used as Basis Functions for Collocation

摘要

Recently a new approach to multivariate (non-tensor product) splines has been introduced which defines a spline space with several attractive properties, including optimal smoothness and high order of approximation. In this paper, we investigate several important components of the application of this theory to the solution of practical problems. In particular, we look at the construction of spline spaces, discuss boundary conditions over a finite domain, and examine the B-spline collocation matrix (giving numerical evidence that it exhibits excellent spectral properties).