## Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations

Jules Kouatchou

### Abstract

We consider the solution of the convection-diffusion equation in two dimensions by a compact high-order 9-point discretization formula combined with multigrid algorithm. We 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.

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### Key words

multigrid method, high-order discretization, asymptotic stability, convection-diffusion equation.

### AMS subject classifications

65F10, 65N06, 65N22, 65N55, 76D07.

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