Free Access
Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1175 - 1199
DOI https://doi.org/10.1051/m2an/2011073
Published online 22 February 2012
  1. R.A. Adams, Sobolev Spaces, 1st edition. Pure Appl. Math. Academic Press, Inc. (1978). [Google Scholar]
  2. W. Bangerth, R. Hartmann and G. Kanschat, deal.II – a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33 (2007) 24/1–24/27. [CrossRef] [Google Scholar]
  3. J.H. Bramble, Multigrid Methods, 1st edition. Longman Scientific & Technical, Essex (1993). [Google Scholar]
  4. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 2nd edition. Springer (2002). [Google Scholar]
  5. H.C. Brinkman, A calculation of the viscouse force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1 (1947) 27–34. [Google Scholar]
  6. T. Chartier, R.D. Falgout, V.E. Henson, J. Jones, T. Manteuffel, S. McCormick, J. Ruge and P.S. Vassilevski, Spectral AMGe (AMGe). SIAM J. Sci. Comput. 25 (2003) 1–26. [CrossRef] [Google Scholar]
  7. M. Dryja, M.V. Sarkis and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math. 72 (1996) 313–348. [CrossRef] [MathSciNet] [Google Scholar]
  8. Y. Efendiev and T.Y. Hou, Multiscale finite element methods, Theory and applications. Surveys and Tutorials in Appl. Math. Sci. Springer, New York 4 (2009). [Google Scholar]
  9. R.E. Ewing, O. Iliev, R.D. Lazarov, I. Rybak and J. Willems, A simplified method for upscaling composite materials with high contrast of the conductivity. SIAM J. Sci. Comput. 31 (2009) 2568–2586. [CrossRef] [Google Scholar]
  10. J. Galvis and Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high-contrast media. Multiscale Model. Simul. 8 (2010) 1461–1483. [Google Scholar]
  11. J. Galvis and Y. Efendiev, Domain decomposition preconditioners for multiscale flows in high contrast media : reduced dimension coarse spaces. Multiscale Model. Simul. 8 (2010) 1621–1644. [Google Scholar]
  12. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Comput. Math. Theory and Algorithms 5 (1986). [Google Scholar]
  13. I.G. Graham, P.O. Lechner and R. Scheichl, Domain decomposition for multiscale PDEs. Numer. Math. 106 (2007) 589–626. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics. Pitman Advanced Publishing Program, Boston, MA 24 (1985). [Google Scholar]
  15. W. Hackbusch, Multi-Grid Methods and Applications, 2nd edition. Springer Series in Comput. Math. Springer, Berlin (2003). [Google Scholar]
  16. T.Y. Hou, X.-H. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 68 (1999) 913–943. [Google Scholar]
  17. A. Klawonn, O.B. Widlund and M. Dryja, Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal. 40 (2002) 159–179 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Mandel and M. Brezina, Balancing domain decomposition for problems with large jumps in coefficients. Math. Comp. 65 (1996) 1387–1401. [CrossRef] [MathSciNet] [Google Scholar]
  19. T.P.A. Mathew, Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations. Lect. Notes Comput. Sci. Eng. Springer, Berlin Heidelberg (2008). [Google Scholar]
  20. S.V. Nepomnyaschikh, Mesh theorems on traces, normalizations of function traces and their inversion. Sov. J. Numer. Anal. Math. Modelling 6 (1991) 151–168. [CrossRef] [Google Scholar]
  21. C. Pechstein and R. Scheichl, Analysis of FETI methods for multiscale PDEs. Numer. Math. 111 (2008) 293–333. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Pechstein and R. Scheichl, Analysis of FETI methods for multiscale PDEs – Part II : interface variation. To appear in Numer. Math. [Google Scholar]
  23. M. Reed and B. Simon, Methods of Modern Mathematical Physics IV : Analysis of Operators. Academic Press, New York (1978). [Google Scholar]
  24. M.V. Sarkis, Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements. Ph.D. thesis, Courant Institute, New York University (1994). [Google Scholar]
  25. M.V. Sarkis, Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. Numer. Math. 77 (1997) 383–406. [CrossRef] [MathSciNet] [Google Scholar]
  26. B.F. Smith, P.E. Bjørstad and W.D. Gropp, Domain Decomposition, Parallel Multilevel Methods for Elliptic Partial Differential Equations, 1st edition. Cambridge University Press, Cambridge (1996). [Google Scholar]
  27. A. Toselli and O. Widlund, Domain Decomposition Methods – Algorithms and Theory. Springer Series in Comput. Math. (2005). [Google Scholar]
  28. J. Van Lent, R. Scheichl and I.G. Graham, Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Numer. Linear Algebra Appl. 16 (2009) 775–799. [CrossRef] [MathSciNet] [Google Scholar]
  29. P.S. Vassilevski, Multilevel block-factrorization preconditioners. Matrix-based analysis and algorithms for solving finite element equations. Springer-Verlag, New York (2008). [Google Scholar]
  30. J. Wang and X. Ye, New finite element methods in computational fluid dynamics by H(div) elements. SIAM J. Numer. Anal. 45 (2007) 1269–1286. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Willems, Numerical Upscaling for Multiscale Flow Problems. Ph.D. thesis, University of Kaiserslautern (2009). [Google Scholar]
  32. J. Xu and L.T. Zikatanov, On an energy minimizing basis for algebraic multigrid methods. Comput. Visualisation Sci. 7 (2004) 121–127. [Google Scholar]

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