V-cycle multigrid for cell-centered finite differences

SIAM Journal of Scientific Computing

Volumn 21, Issue 2, 1999, Pages 552-564

  Kwak, Do Y ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; FINITE VOLUME METHOD; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

CELL CENTERED METHOD; MULTIGRID METHOD;

FINITE DIFFERENCE METHOD;

EID: 0033293110     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597327310     Document Type: Article

References (15)

1. R. BANK AND T. DUPONT, An optimal order process for solving finite element equations, Math. Comp., 36 (1981), pp. 35-51.
2. D. BRAESS AND W. HACKBUSCH, A new convergence proof for the multigrid method including the V-cycle, SIAM J. Numer. Anal., 20 (1983), pp. 967-975.
3. J. H. BRAMBLE, Multigrid Methods, Pitman Res. Notes Math. Ser. 294, Longman Scientific, Harlow, UK, 1993.
4. J. H. BRAMBLE, R. EWING, J. E. PASCIAK, AND J. SHEN, The analysis of multigrid algorithms for cell centered finite difference methods, Adv. Comput. Math., 5 (1996), pp. 15-29.
5. J. H. BRAMBLE AND J. E. PASCIAK, New convergence estimates for multigrid algorithms, Math. Comp., 49 (1987), pp. 311-329.
6. J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, The analysis of multigrid algorithms with non-nested spaces or non-inherited quadratic forms, Math. Comp., 56 (1991), pp. 1-34.
7. A. BRANDT, Guide to multigrid development, in Multigrid Methods, Lecture Notes in Math. 960, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, New York, 1981, pp. 220-312.
8. Z. CAI AND S. MCCORMICK, On the accuracy of the finite volume element method for diffusion equations on composite grids, SIAM J. Numer. Anal., 27 (1990), pp. 636-655.
9. R. E. EWING, R. D. LAZAROV AND P. VASSILEVSKI, Local refinement techniques for elliptic problems on cell-centered grids I, Math. Comp., 56 (1991), pp. 437-461.
10. R. E. EWING AND J. SHEN, A multigrid algorithm for the cell-centered finite difference scheme, in Proceedings 6th Copper Mountain Conference on Multigrid Methods, April 1993, NASA Conference Publication 3224.
11. W. HACKBUSCH, Multi-grid convergence theory, in Multigrid Methods, Lecture Notes in Math. 960, W. Hackbusch and U. Trottenberg, eds., Springer-Verlag, New York, 1981, pp. 177-219.
12. M. KHALIL AND P. WESSELING, Vertex-centered and cell centered multigrid for interface problems, J. Comput. Physics, 98 (1992), pp. 1-10.
13. J. A. MACKENZIE AND K. MORTON, Finite volume solutions of convection-diffusion test problems, Math. Comp., 60 (1992), pp. 189-220.
14. T. F. RUSSELL AND M. F. WHEELER, Finite element and finite difference methods for continuous flows in porous media, in The Mathematics of Reservoir Simulation, R. E. Ewing, ed., SIAM, Philadelphia, 1983, pp. 35-106.
15. P. WESSELING, Cell centered multigrid for interface problems, J. Comput. Phys., 79 (1988), pp. 85-91.