Second order monotone difference schemes with approximation on non-uniform grids for two-dimensional quasilinear parabolic convection-diffusion equations

The present communication is devoted to the construction of monotone difference schemes of the second order of local approximation on non-uniform grids in space for 2D quasilinear parabolic convection-diffusion equation. With the help of difference maximum principle, two-sided estimates of the difference solution are established and an important a priori estimate in a uniform norm C is proved. It is interesting to note that the maximal and minimal values of the difference solution do not depend on the diffusion and convection coefficients.