Free Access
Volume 38, Number 1, January-February 2004
Page(s) 73 - 92
Published online 15 February 2004
  1. 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. Vis. Sci. 1 (1997) 27–40. [CrossRef]
  2. F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173–197. [CrossRef] [MathSciNet]
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  5. 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., NATO ASI Series 39 (1993) 269–286.
  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, H. Brezzi and J.-L. Lions Eds., Pitman, Paris (1994) 13–51.
  7. D. Braess and W. Dahmen, Stability estimates of the mortar finite element method for 3–dimensional problems. East–West J. Numer. Math. 6 (1998) 249–264.
  8. D. Braess, W. Dahmen and C. Wieners, A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal. 37 (1999) 48–69. [CrossRef] [MathSciNet]
  9. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994).
  10. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag, New York (1991).
  11. F. Brezzi and D. Marini, Error estimates for the three-field formulation with bubble stabilization. Math. Comp 70 (2001) 911–934. [CrossRef] [MathSciNet]
  12. F. Brezzi, L. Franca, D. Marini and A. Russo, Stabilization techniques for domain decomposition methods with non-matching grids, in Proc. of the 9th International Conference on Domain Decomposition, P. Bjørstad, M. Espedal and D. Keyes Eds., Domain Decomposition Press, Bergen (1998) 1–11.
  13. A. Buffa, Error estimate for a stabilised domain decomposition method with nonmatching grids. Numer. Math. 90 (2002) 617–640. [CrossRef] [MathSciNet]
  14. J. Gopalakrishnan, On the mortar finite element method. Ph.D. thesis, Texas A&M University (1999).
  15. C. Kim, R.D. Lazarov, J.E. Pasciak and P.S. Vassilevski, Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal. 39 (2000) 519–538. [CrossRef] [MathSciNet]
  16. B.P. Lamichhane and B.I. Wohlmuth, Higher order dual Lagrange multiplier spaces for mortar finite element discretizations. CALCOLO 39 (2002) 219–237. [CrossRef] [MathSciNet]
  17. P. Seshaiyer and M. Suri, Uniform hp convergence results for the mortar finite element method. Math. of Comput. 69 (2000) 521–546. [CrossRef]
  18. R. Stevenson, Locally supported, piecewise polynomial biorthogonal wavelets on non-uniform meshes. Constr. Approx. 19 (2003) 477–508. [CrossRef] [MathSciNet]
  19. C. Wieners and B.I. Wohlmuth, The coupling of mixed and conforming finite element discretizations, in Proc. of the 10th International Conference on Domain Decomposition, J. Mandel, C. Farhat and X. Cai Eds., AMS, Contemp. Math. (1998) 546–553.
  20. C. Wieners and B.I. Wohlmuth, Duality estimates and multigrid analysis for saddle point problems arising from mortar discretizations. SISC 24 (2003) 2163–2184.
  21. B.I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition. Lect. Notes Comput. Sci. 17, Springer, Heidelberg (2001).
  22. B.I. Wohlmuth and R.H. Krause, Multigrid methods based on the unconstrained product space arising from mortar finite element discretizations. SIAM J. Numer. Anal. 39 (2001) 192–213. [CrossRef] [MathSciNet]

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