Free Access
Volume 43, Number 3, May-June 2009
Page(s) 429 - 444
Published online 07 February 2009
  1. Y. Achdou and Yu.A. Kuznetsov, Subtructuring preconditioners for finite element methods on nonmatching grids. J. Numer. Math. 3 (1995) 1–28. [Google Scholar]
  2. Y. Achdou, Yu.A. Kuznetsov and O. Pironneau, Substructuring preconditioner for the Q1 mortar element method. Numer. Math. 71 (1995) 419–449. [CrossRef] [MathSciNet] [Google Scholar]
  3. Y. Achdou, Y. Maday and O.B. Widlund, Iterative substructing preconditioners for mortar element methods in two dimensions. SIAM J. Numer. Anal. 36 (1999) 551–580. [CrossRef] [MathSciNet] [Google Scholar]
  4. F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–198. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements. RAIRO Modél. Math. Anal. Numér. 31 (1997) 289–302. [Google Scholar]
  6. 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, Vol. XI, Collège de France Seminar, H. Brezis and J.L. Lions Eds., Pitman Research Notes in Mathematics Series 299, Longman Scientific & Technical, Harlow (1994) 13–51. [Google Scholar]
  7. D. Braess and W. Dahmen, Stability estimates of the mortar finite element method for 3-dimensional problems. J. Numer. Math. 6 (1998) 249–264. [Google Scholar]
  8. D. Braess, W. Dahmen and C. Wieners, A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37 (2000) 48–69. [Google Scholar]
  9. D. Braess, P. Deuflhard and K. Lipnikov, A subspace cascadic multigrid method for the mortar elements. Computing 69 (2002) 202–225. [Google Scholar]
  10. S. Brenner, Preconditioning complicated finite elements by simple finite elements. SIAM J. Sci. Comput. 17 (1996) 1269–1274. [CrossRef] [MathSciNet] [Google Scholar]
  11. P.G. Ciarlet, The Finite Element Method for Elliptic Problem. North-Holland, Amsterdam (1978). [Google Scholar]
  12. M. Dryja, An iterative substructuring method for elliptic mortar finite element problems with discontinous coefficients, in Domain Decomposition Methods 10, J. Mandel, C. Farhat and X.C. Cai Eds., Contemp. Math. 218 (1998) 94–103. [Google Scholar]
  13. M. Dryja, A. Gantner, O. Widlund and B. Wohlmuth, Multilevel additive Schwarz preconditioner for nonconforming mortar finite element methods. J. Numer. Math. 12 (2004) 23–38. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Gopalakrishnan and J.P. Pasciak, Multigrid for the mortar finite element method. SIAM J. Numer. Anal. 37 (2000) 1029–1052. [CrossRef] [MathSciNet] [Google Scholar]
  15. R.H.W. Hoppe and B. Wohlmuth, Adaptive multilevel iterative techniques for nonconforming finite element discretizations. J. Numer. Math. 3 (1995) 179–198. [Google Scholar]
  16. C. Kim, R. Lazarov, J. Pasciak and P. Vassilevski, Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal. 39 (2001) 519–538. [CrossRef] [MathSciNet] [Google Scholar]
  17. L. Marcinkowski, The mortar element method with locally nonconforming elements. BIT Numer. Math. 39 (1999) 716–739. [CrossRef] [Google Scholar]
  18. L. Marcinkowski, Additive Schwarz method for mortar discretization of elliptic problems with P1 nonconforming finite element. BIT Numer. Math. 45 (2005) 375–394. [CrossRef] [Google Scholar]
  19. L. Marcinkowski and T. Rahman, Neumann – Neumann algorithms for a mortar Crouzeix-Raviart element for 2nd order elliptic problems. BIT Numer. Math. 48 (2008) 607–626. [CrossRef] [Google Scholar]
  20. S.V. Nepomnyaschikh, Fictitious components and subdomain alternating methods. Sov. J. Numer. Anal. Math. Modelling 5 (1990) 53–68. [CrossRef] [Google Scholar]
  21. P. Oswald, Preconditioners for nonconforming elements. Math. Comp. 65 (1996) 923–941. [CrossRef] [MathSciNet] [Google Scholar]
  22. T. Rahman, X. Xu and R. Hoppe, Additive Schwarz method for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients. Numer. Math. 101 (2005) 551–572. [CrossRef] [MathSciNet] [Google Scholar]
  23. T. Rahman, P.E. Bjørstad and X. Xu, Crouzeix-Raviart FE on nonmatching grids with an approximate mortar condition. SIAM J. Numer. Anal. 46 (2008) 496–516. [CrossRef] [Google Scholar]
  24. M. Sarkis, Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Nonconforming Elements. Tech. Report 671, Ph.D. Thesis, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, USA (1994). [Google Scholar]
  25. M. Sarkis, Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using nonconforming elements. Numer. Math. 77 (1997) 383–406. [CrossRef] [MathSciNet] [Google Scholar]
  26. Z.C. Shi and X. Xu, Multigrid for the Wilson mortar element method. Comput. Methods Appl. Math. 1 (2001) 99–112. [MathSciNet] [Google Scholar]
  27. P. Vassilevski and J. Wang, An application of the abstract multilevel theory to nonconforming finite element methods. SIAM J. Numer. Anal. 32 (1995) 235–248. [CrossRef] [MathSciNet] [Google Scholar]
  28. B. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989–1012. [Google Scholar]
  29. B. Wohlmuth, A multigrid method for saddlepoint problems arising from mortar finite element discretizations. Electron. Trans. Numer. Anal. 11 (2000) 43–54. [MathSciNet] [Google Scholar]
  30. J. Xu, Theory of Multilevel Methods. Ph.D. Thesis, Cornell University, USA (1989). [Google Scholar]
  31. J. Xu, Iterative methods by space decomposition and subspace correction. SIAM Rev. 34 (1992) 581–613. [CrossRef] [MathSciNet] [Google Scholar]
  32. J. Xu, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grid. Computing 56 (1996) 215–235. [CrossRef] [MathSciNet] [Google Scholar]
  33. X. Xu and J. Chen, Multigrid for the mortar element method for P1 nonconforming element. Numer. Math. 88 (2001) 381–398. [CrossRef] [MathSciNet] [Google Scholar]
  34. H. Yserentant, Old and new convergence proofs for multigrid methods. Acta Numer. (1993) 285–326. [Google Scholar]
  35. S. Zhang and Z. Zhang, Treatments of discontinuity and bubble functions in the multigrid method. Math. Comp. 66 (1997) 1055–1072. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you