On the Dimension of Bivariate C1 Cubic Spline Space with Homogeneous Boundary Conditions over a CT Triangulation
A bivariate spline is a piecewise polynomial with some smoothness de ned on a parti- tion. In this paper, we mainly study the dimensions of bivariate C1 cubic spline spaces S1;0 3 (CT ) and S1;1 3 (CT ) with homogeneous boundary conditions over CT by using interpolating technique, where CT stands for a CT triangulation. The dimensions are related with the numbers of the inter vertices and the singular boundary vertices. The results of this paper can be applied in many elds such as the nite element method for partial di erential equation, computer aided design, numerical approximation, and so on.
Shaobo Zhong, Yimin Cheng and Xilong Qu
D. X. Gong and F. G. Lang, "On the Dimension of Bivariate C1 Cubic Spline Space with Homogeneous Boundary Conditions over a CT Triangulation", Applied Mechanics and Materials, Vols. 50-51, pp. 488-492, 2011