A Fourth Order Compact Di erence Scheme on

We present a fourth order compact nite diierence scheme on the face centered cubic (FCC) grids for the numerical solution of the two dimensional convection diiusion equation. The seven point formula is deened on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, eecient, and concise. A corresponding multigrid method is developed to solve the resulting sparse linear system. Numerical experiments are conducted to verify the fourth order convergence rate of the derived discretization scheme and to show that the fourth order compact diierence scheme is computationally more eecient than the standard second order central diierence scheme.