Quasi-Interpolating Operators and Their Applications in Hypersingular Integrals

Abstract

The purpose of this paper is to propose and study a class of quasi-interpolating operators in multivariate spline space $S_2^1 (\Delta_{mn}^{2*})$ on non-uniform type-2 triangulation. Based on the operators, we construct cubature formula for two-dimensional hypersingular integrals. Some computing work have been done and the results are quite satisfactory.