Abstract
The importance of spline functions in various fields including numerical fluid dynamics is now well recognized. While basis for univariate spline functions has been well established to be utilized for various problems, surprisingly, until the early eighties, very little information on the theory and computational methods of multivariate spline functions was known. Since then, the subject has become a rapidly growing field of mathematical research. The main purpose of this article is to outline this newly developed theory on multivariate splines. For this, some of the basic topics in univariate splines that have parallel extensions to the multivariate setting are mentioned first.
