Multigrid solution of the advection–diffusion equation with variable coefficients

A multigrid method for the solution of the linear multi‐dimensional advection–diffusion equation with variable coefficients is presented. The method efficiently combines odd–even relaxations with semi‐coarsening. Theoretical and computational convergence rates are given for a large range of advection–diffusion coefficients to demonstrate the efficiency of the method. The construction of the coarse‐grid operator is also discussed in detail since it may have a strong influence on the convergence of the multigrid process when the direction of convection changes.