The Two-Grid Method of Characteristic Finite Volume for Nonlinear Convection Diffusion Equations and Error Estimate

For solving a nonlinear convection diffusion equation,a two-grid method based on the characteristic finite volume solution is proposed in this study.The nonlinearities are expanded about the coarse grid solution uH,and the resulting approximation solution h linear system is solved on a fine grid,Hh.Theoretical analysis and the numerical example result show that,with the same convergence level,this method can eliminate numerical oscillations in the non-linear convection dominated-diffusion problem,simplify the computation and improve the computation efficiency.