Spaces of generalized splines over T-meshes

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 polynom...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 294; pp. 102 - 123
Main Authors: Bracco, Cesare, Roman, Fabio
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2016
Subjects:
Approximation
Approximation power
Basis functions
Computation
Construction
Dimension formula
Generalized splines
Mathematical analysis
Mathematical models
Polynomials
Regularity
Splines
T-mesh
T-mesh
Basis functions
Dimension formula
Generalized splines
41A15
Approximation power
65D07
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary: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.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.08.006