Geodesic
Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations
Electronic transactions on numerical analysis, Tome 6 (1997), pp. 153-161
We consider the solution of the convection-diffusion equation in two dimensions by a compact highorder 9-point discretization formula combined with multigrid algorithm. We prove the -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.
Classification : 65F10, 65N06, 65N22, 65N55, 76D07
Keywords: multigrid method, high-order discretization, asymptotic stability, convection-diffusion equation 
@article{ETNA_1997__6__a9,
     author = {Kouatchou,  Jules},
     title = {Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {153--161},
     year = {1997},
     volume = {6},
     zbl = {0911.65099},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__6__a9/}
}
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EP  - 161
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%A Kouatchou,  Jules
%T Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations
%J Electronic transactions on numerical analysis
%D 1997
%P 153-161
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%U http://geodesic.mathdoc.fr/item/ETNA_1997__6__a9/
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%F ETNA_1997__6__a9
Kouatchou,  Jules. Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations. Electronic transactions on numerical analysis, Tome 6 (1997), pp. 153-161. http://geodesic.mathdoc.fr/item/ETNA_1997__6__a9/