Mathematical analysis of variational isogeometric methods*. (12th May 2014)

• Record Type: Journal Article
• Authors: da Veiga, L. Beirão; Buffa, A.; Sangalli, G.; Vázquez, R.
• Is Part Of: Acta numerica. Volume 23(2014)
• Page Start: 157
• Page End: 287
• Publication Date: 2014-05-12
• Subjects: Numerical analysis -- Periodicals; 518
• DOI: 10.1017/S096249291400004X
• Languages: English
• ISSNs: 0962-4929

Abstract

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.