Dimensions of biquadratic spline spaces over T-meshes

Authors:
Jiansong Deng;Falai Chen;Liangbing Jin
Affiliations:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China;School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China;College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

This paper discusses the dimensions of spline spaces over T-meshes of low degree. Two new concepts are proposed: an extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimensional analysis, the key strategy is linear space embedding with the operator of the mixed partial derivative. A lower bound on the dimension of the biquadratic spline spaces over general T-meshes is provided. Furthermore, by making full use of the level structure of hierarchical T-meshes, a dimension formula of biquadratic spline space over hierarchical T-meshes is proved. Additionally, a topological explanation of the dimension formula is provided.