Two-grid scheme for characteristics finite-element solution of nonlinear convection diffusion problems

A two-grid scheme for characteristics finite-element solution of nonlinear convection-dominated diffusion equations was constructed. The L2 and H1 error estimates of the scheme were derived. A numerical example was also presented. The scheme involves solving one small, nonlinear problem on the coarse-grid system, one linear problem on the fine-grid system. The error estimates and the numerical example show that the new scheme is efficient to the nonlinear convection-dominated diffusion equations.