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@article{Kolev09,
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 title = "{Parallel Auxiliary Space AMG for {H}(curl) Problems}",
 journal = {J. of Computational Mathematics},
 volume = {27}, 
 year = {2009}
}

@MISC{Kolev11,
 author = {Kolev, T. and Vassilevski, P.~S.},
 title = "{Parallel Auxiliary Space AMG Solver for {H}(div) Problems}",
 howpublished = {Technical Report LLNL-JRNL-520391},
 year = {December 15, 2011},
 organization = {Lawrence Livermore National Laboratory}
}


@book{VassilevskiBook,
 author = {Vassilevski, P.~S.},
 title = "{Multilevel Block Factorization Preconditioners}",
 publisher = {Springer},
 address = {New York},
 year = {2008}
}

@article {Mardal2011,
author = {Mardal, K.~A. and Winther, R.},
title = "{Preconditioning discretizations of systems of partial differential equations}",
journal = {Numerical Linear Algebra with Applications},
volume = {18},
number = {1},
publisher = {John Wiley & Sons, Ltd.},
issn = {1099-1506},
url = {http://dx.doi.org/10.1002/nla.716},
doi = {10.1002/nla.716},
pages = {1--40},
keywords = {partial differential equations, finite element methods, discrete systems, preconditioning},
year = {2011},
}


@MISC{metis4,
author = {Karypis, G. and Kumar, V.},
title = {{MeTis: Unstructured Graph Partitioning and Sparse Matrix Ordering System, Version 4.0}},
howpublished = {http://www.cs.umn.edu/~metis},
year = {2009},
organization = {University of Minnesota, Minneapolis, MN},
}


@MISC{Villa2012,
author = {Vassilevski, P.~S. and Villa, U.},
title = "{A mixed formulation for the Brinkman problem}",
howpublished = {submitted to SINUM, available as LLNL-JNRL-563632},
year = {2012},
organization = {Lawrence Livermore National Laboratory}
}

@article{VassilevskiVilla2012,
author = {Vassilevski, P.~S. and Villa, U.},
title = {{A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem}},
journal = {SIAM J. Sci. Comput.},
year = {2012},
note = {accepted}
}

@article{benzi2006augmented,
author = {Benzi, M. and Olshanskii, M.~A.},
collaboration = {},
title = "{An Augmented Lagrangian-Based Approach to the Oseen Problem}",
publisher = {SIAM},
year = {2006},
journal = {SIAM Journal on Scientific Computing},
volume = {28},
number = {6},
pages = {2095-2113},
keywords = {NavierStokes equations; finite element; iterative methods; multigrid; preconditioning},
url = {http://link.aip.org/link/?SCE/28/2095/1},
doi = {10.1137/050646421}
}

@book{fortin1983augmented,
      author       = {Fortin, M. and Glowinski, R.},
      title        = {{Augmented Lagrangian methods: applications to the numerical
                      solution of boundary-value problems}},
      publisher    = {North-Holland},
      address      = {Amsterdam},
      series       = {Studies in Mathematics and its Applications},
      year         = {1983},
      note         = {Transl.of : M\'ethodes de Lagrangian augment\'ees. Paris :
                      Dunod, 1982},
}

@article {Allaire91A,
   author = {Allaire, G.},
   title = "{Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. Abstract framework, a volume distribution of holes}",
   journal = {Archive for Rational Mechanics and Analysis},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0003-9527},
   keyword = {Physics and Astronomy},
   pages = {209-259},
   volume = {113},
   issue = {3},
   url = {http://dx.doi.org/10.1007/BF00375065},
   isbn = {10.1007/BF00375065},
   year = {1991}
}

@article {Allaire91B,
   author = {Allaire, G.},
   title = "{Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes}",
   journal = {Archive for Rational Mechanics and Analysis},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0003-9527},
   keyword = {Physics and Astronomy},
   pages = {261-298},
   volume = {113},
   issue = {3},
   url = {http://dx.doi.org/10.1007/BF00375066},
   isbn = {10.1007/BF00375066},
   year = {1991}
}


@INPROCEEDINGS{hypre_paper,
    author = {Chow, E. and Cleary, A.~J. and Falgout, R.~D.},
    title = "{Design of the hypre Preconditioner Library}",
    booktitle = {In SIAM Workshop on Object Oriented Methods for Inter-operable Scientific and Engineering Computing},
    year = {1998},
    pages = {106--116},
    publisher = {SIAM}
}

@misc{hypre,
key        = {hypre},
title      = "\hypre{}: High Performance Preconditioners",
note       = "{http://www.llnl.gov/CASC/hypre/}"
}

@BOOK{Brezzi1991,
	author = {Brezzi, F and Fortin, M},
	title = {Mixed and Hybrid finite element method},
	publisher = {Springer-Verlag},
	address = {Berlin},
	year = {1991}
}

    @article{1982,
     jstor_articletype = {research-article},
     title = "{Existence, Uniqueness and Approximation for Generalized Saddle Point Problems}",
     author = {Nicolaides, R.~A.},
     journal = {SIAM Journal on Numerical Analysis},
     jstor_issuetitle = {},
     volume = {19},
     number = {2},
     jstor_formatteddate = {Apr., 1982},
     pages = {pp. 349-357},
     url = {http://www.jstor.org/stable/2156950},
     ISSN = {00361429},
     abstract = {Extensions of the well-known results of Brezzi on saddle point problems are presented. The class of problems is generalized to include the unsymmetric case, and the known stability and approximation results are strengthened, and applied to the generalized problem. An application to the solution of certain exterior interface problems is indicated.},
     language = {English},
     year = {1982},
     publisher = {Society for Industrial and Applied Mathematics},
     copyright = {Copyright © 1982 Society for Industrial and Applied Mathematics},
    }

@article {Jennings1999,
	author = "Jennings, A.~A. and Pisipati, R.",
	title = "{The impact of Brinkman's extension of Darcy's law in the neighborhood of a circular preferential flow pathway}",
	journal = "{Environmental Modelling and Software with Environment Data News}",
	volume = "14",
	number = "5",
	year = "1999",
	abstract = "",
	pages = "427-435",
	url = "http://www.ingentaconnect.com/content/els/13648152/1999/00000014/00000005/art00085",
	doi = "doi:10.1016/S1364-8152(98)00085-1"
}


@article{auxspace-xu,
author    = {Xu, J.},
title     = "{The auxiliary space method and optimal preconditioning techniques for unstructured grids}",
journal   = {Computing},
volume    = {56},
number    = {3},
pages     = {215--235},
year      = {1996}
}

@book{Bergh1976,
  title={Interpolation spaces: an introduction},
  author={Bergh, J. and L{\"o}fstr{\"o}m, J.},
  isbn={9783540078753},
  lccn={lc76026487},
  series={Grundlehren der mathematischen Wissenschaften},
  url={http://books.google.co.uk/books?id=jB3vAAAAMAAJ},
  year={1976},
  publisher={Springer-Verlag}
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@InCollection{Babuska1972,
author = {Babu\v{s}ka, I. and Aziz, A.~K.},
title = "{Survey lectures on the mathematical foundations of finite element method}",
booktitle = "{The Mathematical Foundations of the FEM with Application to PDE}",
OPTpages = {•},
publisher = {Academic Press},
year = {1972},
OPTeditor = {Aziz, A. K.},
OPTvolume = {•},
OPTnumber = {•},
OPTseries = {•},
OPTtype = {•},
OPTchapter = {•},
OPTaddress = {New York},
OPTedition = {•},
OPTmonth = {•},
OPTnote = {•},
OPTannote = {•}
}

@book{toselli2005,
  title="{Domain Decomposition Methods--Algorithms and Theory}",
  author={Toselli, A. and Widlund, O.~B.},
  isbn={9783540206965},
  lccn={2004113304},
  series={Springer Series in Computational Mathematics},
  url={http://books.google.com/books?id=tpSPx68R3KwC},
  year={2005},
  publisher={Springer}
}


@incollection {Milani1988,
   author = {Milani, A. and Picard, R.},
   affiliation = {Università di Torino Departmento di Matematica Italia Italia},
   title = "{Decomposition theorems and their application to non-linear electro- and magneto-static boundary value problems}",
   booktitle = "{Partial Differential Equations and Calculus of Variations}",
   series = {Lecture Notes in Mathematics},
   editor = {Hildebrandt, S. and Leis, R.},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {978-3-540-50508-2},
   keyword = {Mathematics and Statistics},
   pages = {317-340},
   volume = {1357},
   url = {http://dx.doi.org/10.1007/BFb0082873},
   doi = {10.1007/BFb0082873},
   year = {1988}
}

@article {Picard1990,
author = {Picard, R.},
title = "{Some decomposition theorems and their application to non-linear potential theory and Hodge theory}",
journal = {Mathematical Methods in the Applied Sciences},
volume = {12},
number = {1},
publisher = {John Wiley & Sons, Ltd},
issn = {1099-1476},
url = {http://dx.doi.org/10.1002/mma.1670120103},
doi = {10.1002/mma.1670120103},
pages = {35--52},
year = {1990},
}

@ARTICLE{Alonso1999,
   author = {{Alonso}, A. and {Valli}, A.},
    title = "{An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations}",
  journal = {Mathematics of Computation},
     year = 1999,
   volume = 68,
    pages = {607-631},
   adsurl = {http://adsabs.harvard.edu/abs/1999MaCom..68..607A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Falk1980,
	author = {Falk, R.~S. and Osborn, J.~E. },
	title = "{Error estimates for mixed methods}",
	series = {RAIRO Anal. Num\'er.},
	volume = 14,
	booktitle = {MR 592753 (82j:65076)},
	pages = {249-277},
	year = {1980}
}

@ARTICLE{Douglas1985,
	author = {Douglas, J.~J. and Roberts, J.~E.},
	title = "{Global estimates for mixed methods for second order elliptic equations}",
	journal = {Math. Comp},
	year = {1985},
        volume = {44},
	pages = {39--52}
}

@ARTICLE{Christiansen2008,
   author = {{Christiansen}, S.~H. and {Winther}, R.},
    title = "{Smoothed projections in finite element exterior calculus}",
  journal = {Mathematics of Computation},
 keywords = {Exterior calculus, finite elements, interpolation operators},
     year = 2008,
    month = jun,
   volume = 77,
    pages = {813-829},
      doi = {10.1090/S0025-5718-07-02081-9},
   adsurl = {http://adsabs.harvard.edu/abs/2008MaCom..77..813C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Guzman2012,
 author = {Guzm\'an, J. and Neilan, M.}, 
 title = "{A family of nonconforming elements for the Brinkman problem}", 
 year = {2012}, 
 doi = {10.1093/imanum/drr040}, 
 URL = {http://imajna.oxfordjournals.org/content/early/2012/01/10/imanum.drr040.abstract}, 
 eprint = {http://imajna.oxfordjournals.org/content/early/2012/01/10/imanum.drr040.full.pdf+html}, 
 journal = {IMA Journal of Numerical Analysis}
}

@article{leTallec1995,
title = {{Domain decomposition with nonmatching grids: augmented Lagrangian approach}},
author = {Le~Tallec, P. and Sassi, T. },
volume = {64},
number = {212},
pages = {1367-1396},
journal = {Math. Comp.},
year = {1995}
}
