An optimal method for high order mixed derivatives of bivariate functions

The problem of optimal recovering high-order mixed derivatives of bivariate functions with finite smoothness is studied. Based on the truncation method, an algorithm for numerical differentiation is constructed, which is order-optimal both in the sense of accuracy and in terms of the amount of involved Galerkin information. Numerical examples are provided to illustrate the fact that our approach can be implemented successfully.
Comment: arXiv admin note: substantial text overlap with arXiv:2309.05425, arXiv:2309.09710, arXiv:2405.20020