Isogeometric Least-squares Collocation Method with Consistency and   Convergence Analysis
  In this paper, we present 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. 
Hongwei Lin and Yunyang Xiong and Xiao Wang and Qianqian Hu
math.NA