Numerical differentiation for two-dimensional scattered data

In this paper, we propose a regularization method for numerical differentiation of two-dimensional mildly scattered input data. A regularized solution is constructed based on the Green's function. The existence and uniqueness of the regularized solution are proved and the convergence estimates are provided under a simple choice of regularization parameter. Numerical results show that our method is quite effective. One of the advantages for our proposed method is that the basis functions are independent of input data.