On generalized moving least squares and diffuse derivatives (Q2902199)

Moving least squares is a practical approximation method which is frequently used in applications where interpolation of given, precise data is not asked for. In this paper, the approximation of function values and derivatives is constructed via the moving least squares method without using the derivatives of the data explicitly. Instead, the derivatives are computed from the moving least squares approach that employs only function values. This turns out to be extremely useful, for example in the numerical evaluation of differential equations related to the finite element method. Error bounds, remarks on the numerical approximation and practical examples are all included as well.