Geodesic
A stable multigrid strategy for convection-diffusion using high order compact discretization
Electronic transactions on numerical analysis, Tome 6 (1997), pp. 211-223.

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Summary: Multigrid schemes based on high order compact discretization are developed for convection-diffusion problems. These multigrid schemes circumvent numerical oscillations and instability, while also yielding higher accuracy. These instabilities are typically exacerbated by the coarser grids in multigrid calculations. Our approach incorporates a 4th order compact formulation for the discretization, while also constructing a consistent multigrid restriction scheme to preserve the accuracy of the fine-to-coarse grid projections. Numerical results demonstrating the higher accuracy and robustness of this approach are presented for representative 2D convection-diffusion problems. These calculations also confirm that our numerical algorithms exhibit the typical multigrid efficiency and mesh-independent convergence properties.
Classification : 65F10, 65N06, 65N22, 65N55
Keywords: convection-diffusion, high-order compact discretizations, multigrid 
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     author = {Pardhanani, Anand L. and Spotz, William F. and Carey, Graham F.},
     title = {A stable multigrid strategy for convection-diffusion using high order compact discretization},
     journal = {Electronic transactions on numerical analysis},
     pages = {211--223},
     publisher = {mathdoc},
     volume = {6},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__6__a5/}
}
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Pardhanani, Anand L.; Spotz, William F.; Carey, Graham F. A stable multigrid strategy for convection-diffusion using high order compact discretization. Electronic transactions on numerical analysis, Tome 6 (1997), pp. 211-223. http://geodesic.mathdoc.fr/item/ETNA_1997__6__a5/