Abstract: For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.

Key words: characteristics finite-element, two-grid method, convergence, convection-diffusion equation