The semidiscrete finite volume element method for nonlinear convection–diffusion problem

In this work, a semidiscrete finite volume element method for the nonlinear convection–diffusion problem is considered. Under some regular assumptions, we obtain the L2 and H1 norm error estimates of numerical solution. Furthermore, we investigate two-grid finite volume element method for the considered equations. Compared with the standard method, the two-grid method is of the same order as the standard method in the H1-norm as long as the mesh sizes satisfy H=Oh13. However, the two-grid method involves much less work than the standard method. Finally, some numerical results are provided to verify the established theoretical analysis.