  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.
