A multigrid algorithm for the mortar finite element method

SIAM Journal on Numerical Analysis

Volumn 37, Issue 1, 2000, Pages 48-69

  Braess, Dietrich ^a   Dahmen, Wolfgang ^b   Wieners, Christian ^c  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Domain decomposition; Mortar method; Saddle point problems; Trace spaces

Indexed keywords

EID: 0000713962     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036142998335431     Document Type: Article

References (24)

1. Y. ACHDOU, F. BEN BELGACEM, C. BERNARDI, AND Y. MADAY, (Book on mortar elements), in preparation.
2. 1 mortar element method, Numer. Math., 71 (1995), pp. 419-449.
3. A. AGOUZAL AND J.-P. THOMAS, Une méthode d'élement finis hybrides en décomposition de domaines, RAIRO Math. Model Anal. Numer. Ser. 2, 29 (1995), pp. 749-764.
4. R. BANK, B. WELFERT, AND H. YSERENTANT, A class of iterative methods for solving saddle point problems, Numer. Math., 56 (1990), pp. 645-666.
5. P. BASTIAN, K. BIRKEN, K. JOHANNSEN, S. LANG, N. NEUSS, H. RENTZ-REICHERT, AND C. WIENERS, UG - a flexible software toolbox for solving partial differential equations, Comput. Visualization Sci., 1 (1997), pp. 27-40.
6. F. BEN BELGACEM, The mortar finite element method with Lagrange multipliers, Numer. Math., to appear.
7. F. BEN BELGACEM AND Y. MADAY, The mortar element method for three dimensional finite elements. RAIRO Math. Model Anal. Numer., 31 (1997), pp. 289-302.
8. C. BERNARDI, Y. MADAY, AND A. T. PATERA, A new nonconforming approach to domain decomposition: The mortar element method, in Nonlinear Partial Differential Equations and Their Applications, H. Brezis and J. L. Lions, eds., Pitman, New York, 1994, pp. 13-51.
9. P. E. BJØRSTAD AND O. B. WIDLUND, Iterative methods for the solution of elliptic problems on regions partitioned in substructures, SIAM J. Numer. Anal., 23 (1986), pp. 1097-1120.
10. D. BRAESS, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, 1997.
11. D. BRAESS AND W. DAHMEN, A cascadic multigrid algorithm for the Stokes equation, Numer. Math., 82 (1999), pp. 179-191.
12. D. BRAESS AND W. DAHMEN, Stability estimates of the mortar finite element method for 3-dimensional problems, East-West J. Numer. Math., 6 (1998), pp. 249-263.
13. D. BRAESS AND R. SARAZIN, An efficient smoother for the Stokes problem, Appl. Numer. Math., 23 (1996), pp. 3-19.
14. D. BRAESS AND R. VERFÜRTH, Multigrid methods for nonconforming finite element methods, SIAM J. Numer. Anal., 27 (1990), pp. 979-986.
15. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.
16. P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Anal. Numér. 9, R-2 (1975), pp. 77-84.
17. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
18. W. HACKBUSCH, Multi-Grid Methods and Applications, Springer-Verlag, Berlin, 1985.
19. J.L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications I, Springer-Verlag, New York, 1972.
20. P. SESHAIYER AND M. SURI, Uniform hp convergence results for the mortar finite element method, Math. Comp., to appear.
21. R. STEVENSON, private communication, University of Utrecht, The Netherlands, 1997.
22. C. WIENERS AND B. WOHLMUTH, The coupling of mixed and conforming finite element discretizations, in Proceedings of the 10th International Conference on Domain Decomposition, J. Mandel, C. Farhat, and X.-C. Cai, eds., Contemp. Math., AMS, Providence, RI, 1998, pp. 546-553.
23. G. WITTUM, On the convergence of multigrid methods with transforming smoothers. Theory with application to the Navier-Stokes equations, Numer. Math., 54 (1989), pp. 543-563.
24. B. WOHLMUTH, Hierarchical a posteriori error estimators for mortar finite element methods with Lagrange multipliers, SIAM J. Numer. Anal., 36 (1999), pp. 1636-1658.