Multiplier spaces for the mortar finite element method in three dimensions

SIAM Journal on Numerical Analysis

Volumn 39, Issue 2, 2002, Pages 519-538

  Kim, Chisup ^a   Lazarov, Raytcho D ^a   Pasciak, Joseph E ^a   Vassilevski, Panayot S ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Domain decomposition; Finite element method; Lagrange multipliers; Mortar

Indexed keywords

EID: 0035322507     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900367065     Document Type: Article

References (34)

1. 1 mortar element method, Numer. Math., 71 (1995), pp. 419-449.
2. Y. ACHDOU, Y. MADAY, AND O. B. WIDLUND, Iterative substructuring preconditioners for mortar element methods in two dimensions, SIAM J. Numer. Anal., 36 (1999), pp. 551-580.
3. G. ANAGNOSTOU, Y. MADAY, C. MAVRIPLIS, AND A. PATERA, On the mortar element method: Generalization and implementation, in Proceedings of the 3rd International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, J. J. Dongarra, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, Philadelphia, 1990.
4. T. ARBOGAST AND I. YOTOV, A non-mortar mixed finite element method for elliptic problems on non-matching multi-block grids, Comput. Methods Appl. Mech. Engrg., 149 (1997), pp. 255-265.
5. F. BEN BELGACEM, The mortar finite element method with Lagrange multiplier, Numer. Math., 84 (1999), pp. 173-197.
6. 2AN Math. Model. Numer. Anal., 31 (1997), pp. 289-302.
7. C. BERNARDI, Y. MADAY, AND A. T. PATERA, Domain decomposition by the mortar element method, in Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters, H.G. Kaper and M. Garbey, eds., Kluwer Academic Publishers, Dordrecht, 1993, pp. 269-286.
8. C. BERNARDI, N. DEBIT, AND Y. MADAY, Coupling finite element and spectral methods: First results, Math. Comp., 54 (1990), pp. 21-39.
9. C. BERNARDI, Y. MADAY, AND A. 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 Res. Notes Math. Ser. 299, Longman Sci. Tech., Harlow, 1994, pp. 13-51.
10. C. BERNARDI, Y. MADAY, AND G. SACCHI-LANDRIANI, Nonconforming matching conditions for coupling spectral finite element methods, Appl. Numer. Math., 54 (1989), pp. 64-84.
11. 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. 249-264.
12. D. BRAESS, W. DAHMEN, AND C. WIENERS, A multigrid algorithm for the mortar finite element method, SIAM J. Numer. Anal., 37 (1999), pp. 48-69.
13. 1 (Ω), Math. Comp., to appear.
14. 2-projections, Math. Comp., 56 (1991), pp. 463-476.
15. S. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Springer-Verlag, Berlin, 1994.
16. 2 projection onto finite element spaces, Math. Comp., to appear.
17. M. CASARIN AND O. B. WIDLUND, A hierarchical preconditioner for the mortar finite element method, Electron. Trans. Numer. Anal., 4 (1996), pp. 75-88.
18. T. F. CHAN, J. J. DONGARRA, R. GLOWINSKI, J. PERIAUX, AND O. B. WIDLUND, EDS., Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1990.
19. T. F. CHAN, R. GLOWINSKI, J. PERIAUX, AND O. B. WIDLUND, EDS., Domain Decomposition Methods, Proceedings of the 2nd International Symposium, Los Angeles, 1988, SIAM, Philadelphia, 1989.
20. P. CLÉMENT, Approximation by finite element functions using local regularization, RAIRO Anal. Numér., 9 (1975), pp. 77-84.
21. 2-projection onto finite element function spaces, Math. Comp., 48 (1987), pp. 521-532.
22. M. R. DORR, On the discretization of interdomain coupling in elliptic boundary-value problems, in Domain Decomposition Methods, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., SIAM, Philadelphia, 1989, pp. 17-37.
23. R. E. EWING, R. D. LAZAROV, T. LIN, AND Y. LIN, The mortar finite volume element methods and domain decompositions, East-West J. Numer. Math., 8 (2000), pp. 93-110.
24. R. GLOWINSKI, G. H. GOLUB, G. A. MEURANT, AND J. PERIAUX, EDS., Proceedings of the 1st International Symposium on Domain Decomposition Methods for Partial Differential Equations, Paris, 1987, SIAM, Philadelphia, 1988.
25. R. GLOWINSKI, YU. A. KUZNETSOV, G. MEURANT, J. PERIAUX, AND O. B. WIDLUND, EDS., Proceedings of the 4th International Symposium on Domain Decomposition Methods for Partial Differential Equations, Moscow, 1990, SIAM, Philadelphia, 1991.
26. J. GOPALAKRISHNAN, On the Mortar Finite Element Method, Ph.D. thesis, Texas A&M University, College Station, TX, 1999.
27. J. GOPALAKRISHNAN AND J. E. PASCIAK, Multigrid for the mortar finite element method, SIAM J. Numer. Anal., 37 (2000), pp. 1029-1052.
28. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Monogr. Stud. Math. 24, Pitman, Boston, 1985.
29. YU. KUZNETSOV AND M. F. WHEELER, Optimal order sub structuring preconditioners for mixed finite element methods on non-matching grids, East-West J. Numer. Math., 3 (1995), pp. 127-143.
30. R. D. LAZAROV. J. E. PASCIAK, AND P. S. VASSILEVSKI, Coupling mixed method and finite volume discretizations of convection-diffusion-reaction equations on non-matching grids, in Proceedings of the 2nd Symposium on Finite Volumes for Complex Applications, Duisburg, Germany, Hermes, 1999, pp. 51-68.
31. J. L. LIONS AND E. MAGENES, Non-homogeneous Boundary Value Problems and Applications, Volume I, Springer-Verlag, Berlin, 1972.
32. P. SESHAIYER AND M. SURI, Uniform hp convergence results for the mortar finite element method, Math. Comp., 69 (2000), pp. 521-546.
33. B.I. WOHLMUTH, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal., 38 (2000), pp. 989-1012.
34. B. I. WOHLMUTH AND R. H. KRAUSE, A multigrid method based on the unconstrained product space for mortar finite element discretizations, SIAM J. Numer. Anal., 39 (2001), pp. 192-213.