The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method

Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency, only a little theoretical results have been established on the numerical analysis of the IGA-C method. In this paper, we deduce the convergence rate of the consistency of the IGA-C method. Moreover, based on the formula of the convergence rate, the necessary and sufficient condition for the consistency of the IGA-C method is developed. These results advance the numerical analysis of the IGA-C method.