This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error estimates in several cases of interest. The theory presented also includes estimates for T-splines, which are an extension of splines allowing for local refinement. In particular, we focus our attention on elliptic and saddle point problems, and we define spline edge and face elements. Our theoretical results are demonstrated by a rich set of numerical examples. Finally, we discuss implementation and efficiency together with preconditioning issues for the final linear system. © Cambridge University Press 2014.

BEIRAO DA VEIGA, L., Buffa, A., Sangalli, G., Vázquez, R. (2014). Mathematical analysis of variational isogeometric methods. ACTA NUMERICA, 23, 157-287 [10.1017/S096249291400004X].

Mathematical analysis of variational isogeometric methods

BEIRAO DA VEIGA, LOURENCO
Primo
;
2014

Abstract

This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error estimates in several cases of interest. The theory presented also includes estimates for T-splines, which are an extension of splines allowing for local refinement. In particular, we focus our attention on elliptic and saddle point problems, and we define spline edge and face elements. Our theoretical results are demonstrated by a rich set of numerical examples. Finally, we discuss implementation and efficiency together with preconditioning issues for the final linear system. © Cambridge University Press 2014.
Articolo in rivista - Articolo scientifico
isogeometric analysis
English
2014
23
157
287
none
BEIRAO DA VEIGA, L., Buffa, A., Sangalli, G., Vázquez, R. (2014). Mathematical analysis of variational isogeometric methods. ACTA NUMERICA, 23, 157-287 [10.1017/S096249291400004X].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98363
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