Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 23, Issue 11, Pages 1979-2003Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500231
Keywords
Isogeometric analysis; T-splines; analysis-suitable; dual-compatible; linear independence; dual basis; partition of unity; approximation estimates; Greville sites.
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Funding
- European Research Council through the FP7 Ideas Starting [205004]
- GeoPDEs - Innovative Compatible Dis-cretization Techniques for Partial Differential Equations
- Italian MIUR through the FIRB Futuro in Ricerca [RBFR08CZ0S]
- Discretizzazioni Isogeometriche per la Meccanica del Continuo
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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. Beiraao da Veiga et al.(5) Analysis-suitable T-splines are dual-compatible which allows for a straightforward construction of a dual basis.
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