Multigrid in H(div) and H(curl)

Numerische Mathematik

Volumn 85, Issue 2, 2000, Pages 197-217

  Arnold, Douglas N ^a   Falk, Richard S ^b   Winther, Ragnar ^c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034386185     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005386     Document Type: Article

References (18)

1. Amrouche, C., Bernardi, C., Dauge, M., Girault, V. (1998): Vector potentials in three-dimensional nonsmooth domains. Math. Methods Appl. Sci. 21, 823-864
2. Arnold, D. N., Falk, R. S., Winther, R. (1997): Preconditioning in H(div) and applications. Math. Comp. 66, 957-984
3. Bossavit, A. (1992): A new viewpoint on mixed elements. Meccanica 27, 3-11
4. Braess, D., Hackbusch, W. (1983): A new convergence proof for the multigrid method including the V-cycle. SIAM J. Numer. Anal. 20, 967-975
5. Bramble, J. H., (1993): Multigrid methods. Pitman Research Notes in Mathematics Series 294
6. Cai, Z., Goldstein, C. I., Pasciak, J. E. (1993): Multilevel iteration for mixed finite element systems with penalty. SIAM J. Sci. Comput. 14, 1072-1088
7. Dryja, M., Widlund, O. B. (1995): Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Comm. Pure Appl. Math 48, 121-155
8. 3. Math. Comp. 51, 55-74
9. Girault, V., Raviart, P-A. (1986) Finite Element Methods for Navier-Stokes Equations. Springer-Verlag
10. Hackbusch, W. (1986): Multigrid Methods and Applications. Springer-Verlag
11. Hiptmair, R. (1997): Multigrid method for H(div) in three dimensions. Electronic Transactions in Numerical Analysis 6, 133-152
12. Hiptmair, R. (1999): Multigrid method for Maxwell's equations. SIAM J. Numer. Anal. 36, 204-225
13. Hiptmair, R., Toselli, A. (1998): Overlapping Schwarz methods for vector valued elliptic problems in three dimensions. In: Parallel solution of PDEs, IMA Volumes in Mathematics and its Applications. Springer-Verlag (to appear)
14. Hiptmair, R. (1999): Canonical construction of finite elements. Math. Comp. 68, 1325-1346
15. 3. Numer. Math. 35, 315-341
16. Smith, P., Björstad, P., Gropp, W. (1996): Domain Decomposition. Cambridge University Press
17. Vassilevski, P. S., Wang, J. (1992) Multilevel iterative methods for mixed finite element discretizations of elliptic problems. Numer. Math. 63, 503-520
18. Xu, J. (1992): Iterative methods by space decomposition and subspace correction. SIAM Review 34, 581-613