Spaces of generalized splines over T-meshes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:294

Article

Bracco, Cesare^1,2  Roman, Fabio² 

[1] Univ Florence, Dept Math & Comp Sci U Dini, I-50134 Florence, Italy

[2] Univ Turin, Dept Math G Peano, I-10123 Turin, Italy

关键词: T-mesh;    Generalized splines;    Dimension formula;    Basis functions;    Approximation power;   

DOI  :  10.1016/j.cam.2015.08.006

来源: Elsevier

【 摘 要 】

We consider a class of non-polynomial spaces, namely a noteworthy case of Extended Chebyshev spaces, and we generalize the concept of polynomial spline space over T-mesh to this non-polynomial setting: in other words, we focus on a class of spaces spanned, in each cell of the T-mesh, both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions on the regularity of the space, a study of the dimension and of the basis, based on the notion of minimal determining set, as well as some results about the dimension of refined and merged T-meshes. Finally, we study the approximation power of the just constructed spline spaces. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free