V-cycle multigrid methods for Wilson nonconforming element

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 43, Issue 7, 2000, Pages 673-684

  Shi, Zhongci ^a   Xu, Xuejun ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Numerical integrations; V cycle multigrid; Wilson element

Indexed keywords

EID: 18144448177     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02878433     Document Type: Article

References (15)

1. Braess, D., Verfurth, R., Multigrid methods for nonconforming finite element methods, SIAM J. Numer. Anal., 1990, 27: 979.
2. Brenner, S. C., An optimal-order multigrid method for P1 nonconforming finite elements, Math. Comp., 1989, 52: 1.
3. 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.
4. Brenner, S. C., An optimal-order nonconforming multigrid method for the biharmonic equation, SIAM J. Numer. Anal., 1989, 26: 1124.
5. Harnish, M. R., Multigrid preconditioning for the biharmonic Direchlet problem, SIAM J. Numer. Anal., 1993, 30: 184.
6. Xu, X. J., Li, L. K., An optimal V-cycle multigrid method for conforming and nonconforming plate elements, Numer. Math. J. Chinese Univer., 1997, 6: 115.
7. 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.
8. 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.
9. Chen, Z. X., Oswald, P., Multigrid and multilever methods rotated Q1 nonconforming finite element, Math. Comp., 1998, 67: 695.
10. Chen, Z. X., On the convergence of Galerkin-multigrid methods for nonconforming finite elements, Technical Report, Texas: Southern Methodist University, 1996.
11. Ciarlet, P. G., The Finite Element Method for Elliptic Problem, Amsterdam: North-Holland, 1978.
12. Bramble, J. H., Kwak, D. Y., Pasciak, J. E., Uniform convergence of multigrid V-cycle iterations for indefinite and non-symmetric problem, SIAM. J. Numer. Anal., 1994, 31: 1746.
13. Xu, J. C., Iterative methods by space decomposition and subspace correction, SIAM Review, 1992, 34: 581.
14. Bramble, J. H., Multigrid Methods, London: Pitman, 1993.
15. 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.