This paper presents the isogeometric least-squares collocation (IGA-L) method, which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense. The number of collocation points employed in IGA-L can be larger than that of the unknowns. Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods. First, a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution. Second, IGA-L method is more flexible and more stable, because the number of collocation points in IGA-L is variable. Third, IGA-L is convergent in some cases of singular parameterization. Moreover, the consistency and convergence analysis are also developed in this paper.

中文翻译：

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具有一致性和收敛性分析的等几何最小二乘配置方法

本文提出了等几何最小二乘搭配（IGA-L）方法，该方法通过使近似微分算子在最小二乘意义上适合真实的微分算子来确定数值解。IGA-L中使用的并置点数可以大于未知数。本文提供的理论分析和数值示例表明，IGA-L优于最新的配置方法。首先，IGA-L中并置点数的少量增加导致其数值解的精度大大提高。第二，IGA-L方法更灵活，更稳定，因为IGA-L中的并置点数是可变的。第三，在某些单一参数设置情况下，IGA-L收敛。此外，