A new cascadic multigrid
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Abstract
We present a new cascadic multigrid for elliptic problems.
Keywords
cascadic multigrid finite element elliptic problemsPreview
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References
- 1.Bornemann, F., Deuflhard, P., The cascadic multigrid method for elliptic problems, Numer. Math., 1996, 75: 135.MATHCrossRefMathSciNetGoogle Scholar
- 2.Bornemann, F., Deuflhard, P., The cascadic multigrid method, The Eighth International Conference on Domain Decomposition Methods for Partial Differential Equations ( eds. Glowinski, R., Periaux, J., Shi, Z. et al. ), New York: John Wiley and Sons, 1997.Google Scholar
- 3.Bornemann, F., Krause, R., Classical and cascadic multigrid-methodogical comparison, Proceedings of the 9th International Conference on Domain Decomposition ( eds. Bjorstad, P., Espedal, M., Keyes, D.), New York: John Wiley and Sons, 1998.Google Scholar
- 4.Shaidurov, V., Some estimates of the rate of convergence for the cascadic conjugate gradient method, Comp. Math. Applic., 1996, 31: 161.MATHCrossRefMathSciNetGoogle Scholar
- 5.Shi, Z., Xu, X., Cascadic multigrid method for the second order elliptic problem, East-West J. Numer. Math., 1998, 6: 309.MATHMathSciNetGoogle Scholar
- 6.Shi, Z., Xu, X., Cascadic multigrid for elliptic problems, East-West J. Numer. Math., 1999, 7: 199.MATHMathSciNetGoogle Scholar
- 7.Shi, Z., Xu, X., Cascadic multigrid method for the plate bending problem, East-West J. Numer. Math., 1998, 6: 137.MATHMathSciNetGoogle Scholar
- 8.Braess, D., Dahmen, W., A cascade multigrid algorithm for the Stokes equations, Number. Math., 1999, 82: 179.MATHCrossRefMathSciNetGoogle Scholar
- 9.Shi, Z., Xu, X., Cascadic multigrid for parabolic problems, J. Comput. Math., 2000, 18: 450.MathSciNetGoogle Scholar
- 10.Ciarlet, P.,The Finite Element Method for Elliptic Problems, Amsterdam: North-Holland, 1978.Google Scholar
- 11.Zienkiewicz, O. C., The Finite Element Method, 3rd. ed., London: McGraw-Hill, 1977.MATHGoogle Scholar
- 12.Powell, M. J. D., Sabin, M. A., Piecewise quadratic approximations on triangles, ACM Trans. Mat. Software, 1977, 3: 316.MATHCrossRefMathSciNetGoogle Scholar
- 13.Xu, J., The auxiliary space method and optimal multigrid precondition techniques for unstructured grids, Computing, 1996, 56: 215.MATHCrossRefMathSciNetGoogle Scholar
- 14.Bank, R., Dupont, T., An optimal order process for solving finite element equations, Math. Comput., 1980, 36: 35.MathSciNetGoogle Scholar
- 15.Brenner, S., Convergence of nonconforming multigrid methods without full elliptic regularity, Math. Comp., 1998, 68: 25.CrossRefMathSciNetGoogle Scholar
- 16.Bramble, J., Multigrid Methods, England: Pitman, 1993.MATHGoogle Scholar
- 17.Kloucek, P., Li, B., Luskin, M., Analysis of a class of nonconforming finite elements for crystalline microstructures, Math. Comp., 1996, 65: 1111.MATHCrossRefMathSciNetGoogle Scholar
- 18.Shi, Z., Convergence of the TRUNC plate element, Comp. Meth. Appl. Mech. Engrg., 1987, 62: 71.MATHCrossRefGoogle Scholar
- 19.Shi, Z., On convergence of the incomplete biquadratic nonconforming plate element, Math. Numer. Sinica (in Chinese), 1988, 8: 53.Google Scholar
- 20.Shi, Z., Chen, S., Huang, H., Plate elements with high accuracy, in Collec. Geom. Anal. Math. Phys. ( ed. Li Ta-Tsien), Singapore: World Scientific, 1997, 155–164.Google Scholar
- 21.Shi, Z., Chen, Q., A rectangular plate element with high accuracy, Science in China (in Chinese), Ser. A, 2000, 30(6): 504.Google Scholar
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