Difference schemes on nonuniform grids for the two-dimensional convection-diffusion equation

New second-order accurate monotone difference schemes on nonuniform spatial grids for two-dimensional stationary and nonstationary convection-diffusion equations are proposed. The monotonicity and stability of the solutions of the computational methods with respect to the boundary conditions, the initial condition, and the right-hand side are proved. Two-sided and corresponding a priori estimates are obtained in the grid norm of $C$. The convergence of the proposed algorithms to the solution of the original differential problem with the second order is proved.