Asymptotic Stability of a 9-Point Multigrid Algorithm
for
Convection-Diffusion Equations


Jules Kouatchou


We consider the solution of the convection-diffusion equation in two dimension by a compact high-order 9-point discretization formula combined with multigrid algorithm. We analytically prove the $\epsilon$-asymptotic stability of the coarse grid operators. Two strategies are examined. A method to compute the asymptotic convergence is described and applied to the multigrid algorithm.