@article{ZVMMF_2004_44_8_a9,
author = {M. A. Ol'shanskii},
title = {An analysis of the multigtrid method for the convection-diffusion equations with the {Dirichlet} boundary conditions},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1450--1479},
year = {2004},
volume = {44},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a9/}
}
TY - JOUR AU - M. A. Ol'shanskii TI - An analysis of the multigtrid method for the convection-diffusion equations with the Dirichlet boundary conditions JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2004 SP - 1450 EP - 1479 VL - 44 IS - 8 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a9/ LA - ru ID - ZVMMF_2004_44_8_a9 ER -
%0 Journal Article %A M. A. Ol'shanskii %T An analysis of the multigtrid method for the convection-diffusion equations with the Dirichlet boundary conditions %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2004 %P 1450-1479 %V 44 %N 8 %U http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a9/ %G ru %F ZVMMF_2004_44_8_a9
M. A. Ol'shanskii. An analysis of the multigtrid method for the convection-diffusion equations with the Dirichlet boundary conditions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 8, pp. 1450-1479. http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_8_a9/
[1] Fedorenko R. P., “O skorosti skhodimosti odnogo iteratsionnogo protsessa”, Zh. vychisl. matem. i matem. fiz., 4:3 (1964), 559–564 | MR | Zbl
[2] Bakhvalov N. S., “O skhodimosti odnogo relaksatsionnogo metoda pri estestvennykh ogranicheniyakh na ellipticheskii operator”, Zh. vychisl. matem. i matem. fiz., 6:5 (1966), 861–883 | Zbl
[3] Brandt A., “Multi-level adaptive solutions to boundary value problems”, Math. Comput., 31 (1977), 333–390 | DOI | MR | Zbl
[4] Olshanskii M. A., Lektsii i uprazhneniya po mnogosetochnym metodam, TsPI mekhan.-matem. f-t MGU, M., 2003
[5] Shaidurov V. V., Mnogosetochnye metody konechnykh elementov, Nauka, M., 1989 | MR
[6] Bramble J. H., Multigrid methods, Longman, Harlow, 1993 | MR | Zbl
[7] Hackbusch W., Multi-Grid Methods and Applications, Springer, Berlin, 1985 | Zbl
[8] Bey J., Wittum G., “Downwind numbering: robust multigrid for convection-diffusion problems”, Appl. Numer. Math., 23 (1997), 177–192 | DOI | MR | Zbl
[9] Hackbusch W., Probst T., “Downwind Gauss-Seidel smoothing for convection dominated problems”, Numer. Linear Algebra Appl., 4 (1997), 85–102 | 3.0.CO;2-2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[10] Johannsen K., Robust smoothers for convection-diffusion problems, Preprint IWR, University of Heidelberg, 1999
[11] Mulder W., “A new multigrid approach to convection problems”, J. Comput. Phys., 83 (1989), 303–323 | DOI | MR | Zbl
[12] Naik N. H., van Rosedale J., “The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids”, SIAM Numer. Analys., 30 (1993), 215–229 | DOI | MR | Zbl
[13] Reusken A., “Multigrid with matrix-dependent transfer operators for convection-diffusion problems”, Multigrid Methods, Proc. of the fourth multigrid Conf., v. 4, Int. Ser. Numer. Math., 116, 1994, 269–280 | MR | Zbl
[14] Zeeuw P. M. de, “Matrix-dependent prolongations and restrictions in a blackbox multigrid solver”, J. Comput. Appl. Math., 33 (1990), 1–27 | DOI | MR | Zbl
[15] Bramble J. H., Pasciak J. E., Xu J., “The analysis of multigrid algorithms for nonsymmetric and indefinite problems”, Math. Comput., 51 (1988), 389–414 | DOI | MR | Zbl
[16] Mandel J., “Multigrid convergence for nonsymmetric, indefinite variational problems and one smoothing step”, Appl. Math. Comput., 19 (1986), 201–216 | DOI | MR | Zbl
[17] Wang J., “Convergence analysis of multigrid algorithms for nonselfadjoint and indefinite elliptic problems”, SIAM J. Numer. Analys., 30 (1993), 275–285 | DOI | MR | Zbl
[18] Persson I., Samuelsson K., Szepessy A., “On the convergence of multigrid methods for flow problems”, Electron. Trans. Numer. Analys., 8 (1999), 46–87 | MR | Zbl
[19] Reusken A., “Fourier analysis of a robust multigrid method for convection-diffusion equations”, Numer. Math., 71 (1995), 365–397 | DOI | MR | Zbl
[20] Bank R. E., Benbourenane M., “The hierarchical basis multigrid method for convection-diffusion equations”, Numer. Math., 61 (1992), 7–37 | DOI | MR | Zbl
[21] Reusken A., “Convergence analysis of a multigrid method for convection-diffusion equations”, Numer. Math., 91 (2002), 323–349 | DOI | MR | Zbl
[22] Olshanskii M. A., Reusken A., “Convergence analysis of a multigrid method for a convection-dominated model problem”, SIAM J. Num. Anal., 2004 | MR
[23] Roos H.-G., Stynes M., Tobiska L., Numerical Methods for Singularly Perturbed Differential Equations, Springer, Berlin, 1996 | MR
[24] Zhou G., “How accurate is the streamline diffusion finite element method”, Math. Comput., 66 (1997), 31–44 | DOI | MR | Zbl
[25] Ramage A., “A multigrid preconditioner for stabilised discretization of advection-diffusion problem”, J. Comput. Appl. Math., 110 (1999), 187–223 | DOI | MR
[26] Johnson C., Schatz A. H., Wahlbin L. B., “Crosswind smear and pointwise errors in streanline diffusion finite element methods”, Math. Comput., 49 (1987), 25–38 | DOI | MR | Zbl
[27] Eriksson K., Johnson C., “Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems”, Math. Comput., 60 (1993), 167–188 | DOI | MR | Zbl
[28] Grisvard P., Elliptic problems in nonsmooth domains, Pitman, London, 1985 | MR | Zbl
[29] Wahlbin L. B., “Local behavior in finite element methods”, Handbook of Numerical Analysis, v. II, Finite element methods, North-Holland, Amsterdam, 1991, 353–522 | MR | Zbl
[30] Niijima K., “Poinwise error estimates for a streamline diffusion finite element scheme”, Numer. Math., 56 (1990), 707–719 | DOI | MR | Zbl
[31] Stevenson R. P., “New estimates of the contraction number of $\mathrm{V}$-cycle multi-grid with applications to anisotropic equations”, Incomplete Decompositions, Proc. eight GAMM Seminar, Notes on Numerical Fluid Mech., 41, 1993, 159–167 | MR | Zbl
[32] Stevenson R. P., “Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners”, Numer. Math., 66 (1993), 373–398 | DOI | MR | Zbl
[33] Wittum G., “On the robustness of ILU smoothing”, SIAM J. Sci. Statist. Comput., 10 (1989), 699–717 | DOI | MR | Zbl
[34] Olshanskii M. A., Reusken A., “On the convergence of a multigrid method for linear reaction-diffusion problem”, Computing, 65 (2000), 193–202 | DOI | MR | Zbl
[35] Olshanskii M. A., Reusken A., “Navier-Stokes equations in rotation form: A robust multigrid solver for the velocity problem”, SIAM J. Sci. Comput., 23 (2002), 1683–1706 | DOI | MR | Zbl
[36] Hackbusch W., Iterative solution of large sparse systems of equations, Springer, New York, 1994 | MR