Mathematical analysis of variational isogeometric methods

被引：202

作者：

da Veiga, L. Beirao ^{[1
,2
]}

Buffa, A. ^{[2
]}

Sangalli, G. ^{[2
,3
]}

Vazquez, R. ^{[2
]}

机构：

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] E Magenes CNR, Ist Matemat Applicata & Tecnol Informat, I-27100 Pavia, Italy

[3] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

ACTA NUMERICA | 2014年 / 23卷

基金：

欧洲研究理事会;

关键词：

FLUID-STRUCTURE INTERACTION; CONFORMING B-SPLINES; ELEMENT EXTERIOR CALCULUS; SUITABLE T-SPLINES; FINITE-ELEMENTS; NONLINEAR ELASTICITY; COMPUTATIONAL DOMAIN; LINEAR INDEPENDENCE; LOCAL REFINEMENT; NURBS;

D O I：

10.1017/S096249291400004X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：157 / 287

页数：131

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