Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme

A numerical method for solving elliptic differential equations (on unstructured computational grids) is described, which is based on a nonlinear compact-polynomial computational scheme. For this purpose, an approximate transition from the elliptic equation to the hyperbolic type of equations was carried out in the work. To find the solution of the hyperbolic version of the diffusion equation, a transition (in the vicinity of the computational cell Ωi) to a local curvilinear coordinate system was performed, a nonlinear compact-polynomial computational scheme was used (the "predictor" stage), and the control volume method was applied (the "corrector" stage). The results of initial testing (on problems of different physical nature) of the proposed numerical method are presented.