Numerical solution of mixed boundary value problem for some nonlinear elliptic equation

The mixed boundary value problem for nonlinear elliptic equation-∇k(∣∇u∣2)∇u=F(x,y),(x,y)∈Ω,u=0,(x,y)∈Γ1⊂∂Ω,k(∣∇u∣2)∂u∂n=ϕ(x,y),(x,y)∈Γ2⊂∂Ωis considered. The finite difference scheme is obtained via rectangular finite elements and is compared with classical finite difference scheme.