Abstract
In this paper, we propose a theoretical study of the approximation properties of NURBS spaces, which are used in Isogeometric Analysis. We obtain error estimates that are explicit in terms of the mesh-size h, the degree p and the global regularity, measured by the parameter k. Our approach covers the approximation with global regularity from C 0 up to C k–1, with 2k − 1 ≤ p. Notice that the interesting case of higher regularity, up to k = p, is still open. However, our results give an indication of the role of the smoothness k in the approximation properties, and offer a first mathematical justification of the potential of Isogeometric Analysis based on globally smooth NURBS.
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Beirão da Veiga, L., Buffa, A., Rivas, J. et al. Some estimates for h–p–k-refinement in Isogeometric Analysis. Numer. Math. 118, 271–305 (2011). https://doi.org/10.1007/s00211-010-0338-z
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DOI: https://doi.org/10.1007/s00211-010-0338-z