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, LOURENCO
Primo
;
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.
Articolo in rivista - Articolo scientifico
isogeometric analysis
English
271
305
35
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].
BEIRAO DA VEIGA, L; Buffa, A; Rivas, J; Sangalli, G
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98844
Citazioni
  • Scopus 143
  • ???jsp.display-item.citation.isi??? 124
Social impact