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.
BEIRAO DA VEIGA, L., Buffa, A., Rivas, J., Sangalli, G. (2011). Some estimates for h-p-k-refinement in Isogeometric Analysis. NUMERISCHE MATHEMATIK, 118(2), 271-305 [10.1007/s00211-010-0338-z].
Some estimates for h-p-k-refinement in Isogeometric Analysis
BEIRAO DA VEIGA, LOURENCOPrimo
;
2011
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.