Preconditioned iterative methods and finite difference schemes for convection-diffusion

We conduct experimental study on numerical solution of the two dimensional convection-diiusion equation discretized by three nite diierence schemes: the traditional central diier-ence scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coeecient matrices arising from diierent schemes and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.