Modified Shepard's method by six-points local interpolant

In this paper, we present an improvement of the Hexagonal Shepard method which uses functional and first order derivative data. More in details, we use six-point basis functions in combination with the modified local interpolant on six-points. The resulting operator reproduces polynomials up to degree 3 and has quartic approximation order. Several numerical results show the good accuracy of approximation of the proposed operator.

Automated summary

The paper presents an improvement of the Hexagonal Shepard method, utilizing functional and first order derivative data. By using six-point basis functions and a modified local interpolant, the resulting operator can reproduce polynomials up to degree 3 and has quartic approximation order. The numerical results demonstrate the good accuracy of the proposed operator.