Multigrid method for nonconforming FE-discretizations with application to non-matching grids

Computing (Vienna/New York)

Volumn 63, Issue 1, 1999, Pages 1-25

  Braess, D ^a   Dryja, M ^b   Hackbusch, W ^c  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF WARSAW   (Poland)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS;

MULTIGRID METHOD;

FINITE ELEMENT METHOD;

EID: 0032653914     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006070050048     Document Type: Article

References (15)

1. Ben Belgacem, F.: The mortar element method with Lagrange multipliers. Numer. Math. (to appear).
2. 2AN 31, 289-302 (1997).
3. Bernardi, C., Maday, Y., Patera, A. T.: A new nonconforming approach to domain decomposition: the mortar element method. In: Nonlinear partial differential equations and their applications (Brezis, H., Lions, J. L., eds.), pp. 13-51. New York: Pitman 1994.
4. Braess, D.: Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge: Cambridge University Press 1997.
5. Braess, D., Verfürth, R.: Multi-grid methods for nonconforming finite element methods. SIAM J. Numer. Anal. 27, 979-986 (1990).
6. Braess, D., Dahmen, W.: Stability estimates of the mortar finite element method for 3-dimensional problems. East-West J. Numer. Math. 6, 249-264 (1998).
7. Braess, D., Dahmen, W., Wieners, C.: A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. (to appear).
8. Brenner, S.: An optimal order multigrid method for P1 nonconforming finite elements. Math. Comput. 32, 1-15 (1989).
9. Dryja, M.: An iterative substructuring method for elliptic mortar finite element problems with discontinuous coefficients. In: Domain decomposition methods 10 (Mandel, J., Farhat, Ch., Cai, X-C., eds.), pp. 94-103. Contemporary Mathematics, vol. 218.
10. Dryja, M.: Additive Schwarz methods for elliptic mortar finite element problems. In: Modeling and optimization of distributed parameter systems, applications to engineering (Malanowski, K., Nahorski, Z., Peszynska, M., eds.), pp. 31-50. London: Chapman & Hall 1996.
11. Gopalakrishnan, J., Pasciak, J. E.: Multigrid for the mortar finite element method. Report ISC-98-04-MATH, Texas A&M University, 1998.
12. Hackbusch, W.: Multi-grid methods and applications. Berlin Heidelberg New York: Springer 1985.
13. Hackbusch, W.: Elliptic differential equations. Theory and numerical treatment. Berlin Heidelberg New York Tokyo: Springer 1992.
14. Stevenson, R.: The Cascade iteration for nonconforming discretisations. Report 9803 University of Nijmegen, Feb. 1998.
15. Brenner, S.: Convergence of nonconforming multigrid methods without full elliptic regularity. Mat. Comp. 68, 25-53 (1999).