Articolo in rivista, 2011, ENG, 10.1007/s00211-010-0338-z

Some estimates for h-p-k-refinement in isogeometric analysis

L. Beirao da Veiga, A. Buffa, J. Rivas, and G. Sangalli

Dipartimento di Matematica, Università di Pavia; Dipartimento Matematica F Enriques, Milano; Ist Matemat Applicata & Tecnol Informatiche del CNR, Pavia; Univ. Pais Vasco Euskal Herriko Unibertsitatea, Dept Matemat, Leioa 48940, Bizkaia, Spain .

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 a parts per thousand currency sign 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.

Numerische Mathematik 118 , pp. 271–305

Keywords

Finite elements, Error bounds, NURBS, Approximations

CNR authors

Beirao Da Veiga Lourenco, Sangalli Giancarlo, Rivas Judith, Buffa Annalisa

CNR institutes

IMATI – Istituto di matematica applicata e tecnologie informatiche "Enrico Magenes"