Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-01

Journal: JOURNAL OF COMPUTATIONAL MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 33

Issue: 3

Page Number: 248-262

ISSN: 0254-9409

Key Words: Spline space; Smoothing cofactor-conformality method; Instability in the dimension; T-meshes

Abstract: 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.