Numerical integration based on a multilevel quartic quasi-interpolation operator

Quasi-interpolation is very important in the study of the scattered data approximation, numerical integration and numerical solutions of differential equations. In this paper, we proposed a multilevel quasi-interpolation scheme by using B-spline basis functions on quartic spline space. Moreover, the proposed scheme is applied to the numerical integration of two-dimensional singular integrals. Some numerical results with contrast to the existing methods are provided.