Some estimates for h–p–k-refinement in Isogeometric Analysis

Authors:
L. Beirão da Veiga;A. Buffa;J. Rivas;G. Sangalli
Affiliations:
Dipartimento di Matematica “F. Enriques”, Via Saldini, 50, 20133, Milano, Italy;Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Via Ferrata, 1, 27100, Pavia, Italy;Universidad del País Vasco-Euskal Herriko Unibertsitatea, Departamento de Matemáticas, Barrio Sarriena s/n, 48940, Leioa (Bizkaia), Spain;Università di Pavia, Dipartimento di Matematica, Via Ferrata, 1, 27100, Pavia, Italy
Venue:
Numerische Mathematik
Year:
2011

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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.