Mathematical analysis of variational isogeometric methods

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...

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Bibliographic Details
Published in:Acta numerica 2014-05, Vol.23, p.157-287
Main Authors: da Veiga, L. Beirão, Buffa, A., Sangalli, G., Vázquez, R.
Format: Article
Language:English
Subjects:
Approximation
Error analysis
Estimates
Linear algebra
Linear systems
Mathematical analysis
Optimization
Saddle points
Splines
Theoretical mathematics
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Summary: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.
ISSN:0962-4929
1474-0508
DOI:10.1017/S096249291400004X