### ON THE PROBLEM OF INSTABILITY IN THE DIMENSIONS OF SPLINE SPACES OVER T-MESHES WITH T-CYCLES

Qing-Jie Guo, Ren-Hong Wang, Chong-Jun Li

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
• Received:2013-08-07 Revised:2014-11-17 Online:2015-05-15 Published:2015-05-15
• Supported by:

This work is partly supported by the National Natural Science Foundation of China (Nos. 11290143, U1135003, 11471066, 11271060, 11301052), Fundamental Research of Civil Aircraft (No. MJ-F-2012-04), and the Fundamental Research Funds for the Central Universities (Nos. DUT13LK07, DUT13LK45, DUT14YQ111).

Qing-Jie Guo, Ren-Hong Wang, Chong-Jun Li. ON THE PROBLEM OF INSTABILITY IN THE DIMENSIONS OF SPLINE SPACES OVER T-MESHES WITH T-CYCLES[J]. Journal of Computational Mathematics, 2015, 33(3): 248-262.

The T-meshes are local modification of rectangular meshes which allow T-junctions. The splines over T-meshes are involved in many fields, such as finite element methods, CAGD etc. The dimension of a spline space is a basic problem for the theories and applications of splines. However, the problem of determining the dimension of a spline space is difficult since it heavily depends on the geometric properties of the partition. In many cases, the dimension is unstable. In this paper, we study the instability in the dimensions of spline spaces over T-meshes by using the smoothing cofactor-conformality method. The modified dimension formulas of spline spaces over T-meshes with T-cycles are also presented. Moreover, some examples are given to illustrate the instability in the dimensions of the spline spaces over some special meshes.

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