T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence of the blending functions and optimal approximation properties of the associated T-spline space. These are corollaries of our main result: A T-mesh is analysis-suitable if and only if it is dual-compatible. Indeed, dual compatibility is a concept already defined and used in L. Beirão da Veiga et al.5 Analysis-suitable T-splines are dual-compatible which allows for a straightforward construction of a dual basis.

Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties / L. Beirao da Veiga, A. Buffa, G. Sangalli, R. Vazquez. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 23:11(2013 Oct), pp. 1979-2003. [10.1142/S0218202513500231]

Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties

L. Beirao da Veiga;
2013-10

Abstract

T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear independence of the blending functions and optimal approximation properties of the associated T-spline space. These are corollaries of our main result: A T-mesh is analysis-suitable if and only if it is dual-compatible. Indeed, dual compatibility is a concept already defined and used in L. Beirão da Veiga et al.5 Analysis-suitable T-splines are dual-compatible which allows for a straightforward construction of a dual basis.
Isogeometric analysis ; T-splines ; analysis-suitable ; dual-compatible ; linear independence; dual basis ; partition of unity ; approximation estimates ; Greville sites
Settore MAT/08 - Analisi Numerica
MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/224697
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