Abstract
Here two types of optimal V-cycle multigrid algorithms are presented for Wilson nonconforming finite element.
Similar content being viewed by others
References
Braess, D., Verfurth, R., Multigrid methods for nonconforming finite element methods, S1AM J. Numer. Anal., 1990,27: 979.
Brenner, S. C., An optimal-order multigrid method for PI nonconforming finite elements, Math. Comp., 1989, 52: 1.
Vassilevski, P. S., Wang, J. P., An application of the abstract multilevel theory to nonconforming finite element methods, SIAM J. Numer. Anal., 1995, 32: 235.
Brenner, S. C, An optimal-order nonconforming multigrid method for the biharmonic equation, S1AM J. Numer. Anal., 1989, 26: 1124.
Harnish, M. R., Multigrid preconditioning for the biharmonic Dirichlet problem, SIAM J. Numer. Anal., 1993, 30: 184.
Xu, X. J., Li, I,. K., An optimal V-cycle multigrid method for conforming and nonconforming plate elements, Numer. Math. J. Chinese Univer., 1997, 6: 115.
Shi, Z.C.., Jiang, B., Multigrid method for Wilson nonconforming finite element with numerical integration, Domain Decomposition Methods and Related Topics, Symposium of Research Institute for Mathematical Sciences, Kyoto: Kyoto University, 1996, 103–121.
Bramble, J. H., Goldstein, C. L., Pasciak, J. H., Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature, SIAM J. Sci. Comput., 1994, 15: 566.
Chen, Z. X., Oswald, P., Multigrid and multilevel methods rotated Ql nonconforming finite element, Math. Comp., 1998, 67: 695.
Chen, Z. X., On the convergence of Galerkin-multigrid methods for nonconforming finite elements, Technical Report, Texas: Southern Methodist University, 1996.
Ciarlet, P. G., The finite Element Method for Elliptic Problem, Amsterdam: North-Holland, 1978.
Bramble, J. H., Kwak, D. Y., Pasciak, J. E., Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problem, S1AM. J. Numer. Anal., 1994, 31: 1746.
Xu, J. C., Iterative methods by space decomposition and subspace correction, SI AM Review, 1992, 34: 581.
Bramble, J. H., Multigrid Methods, London: Pitman, 1993.
Bramble, J. H., Pasciak, J. E., Xu, J. C., The analysis of multigrid algorithms with nonnested spaces and noninherited quadratic forms, Math. Comp.1991, 56: 1.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shi, Z., Xu, X. V-cycle multigrid methods for Wilson nonconforming element. Sci. China Ser. A-Math. 43, 673–684 (2000). https://doi.org/10.1007/BF02878433
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02878433