
%% Created for Jakob Suckale at 2007-09-06 11:30:44 +0200 


%% Saved with string encoding Unicode (UTF-8) 
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@Unpublished{VeVi1,
 author = {A Veneziani and U Villa},
 title = {ALADINS: an ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations},
 note = {in preparation},
 OPTkey = {},
 OPTmonth = {},
 year = {2011},
 OPTannote = {},
 OPTurl = {},
 OPTdoi = {},
 OPTissn = {},
 OPTlocalfile = {},
 OPTabstract = {},
}

@Unpublished{VeVi2,
 author = {A Veneziani and U Villa},
 title = {On the solution of the discrete Laplace finite element pressure operator with direct methods},
 note = {in preparation},
 OPTkey = {},
 OPTmonth = {},
 year = {2011},
 OPTannote = {},
 OPTurl = {},
 OPTdoi = {},
 OPTissn = {},
 OPTlocalfile = {},
 OPTabstract = {},
}

% Panayot
@article{Acosta2008,
   author = {{Acosta}, G. and {Apel}, T. and {Dur{\'a}n}, R.~G. and {Lombardi}, A.~L.
	},
    title = "{Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {0809.2072},
 primaryClass = "math.NA",
 keywords = {Mathematics - Numerical Analysis, 65N30},
     year = 2008,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2008arXiv0809.2072A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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@unpublished{Arnold2011,
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@article {Babuska1970,
    AUTHOR = {Babu{\v{s}}ka, Ivo},
     TITLE = {Error-bounds for finite element method},
   JOURNAL = {Numer. Math.},
  FJOURNAL = {Numerische Mathematik},
    VOLUME = {16},
      YEAR = {1970/1971},
     PAGES = {322--333},
      ISSN = {0029-599X},
   MRCLASS = {65.66},
  MRNUMBER = {0288971 (44 \#6166)},
MRREVIEWER = {F. Odeh},
}

@article{Braack2001,
title = "{Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations}",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "9-12",
pages = "1126 - 1136",
year = "2011",
note = "",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2010.06.034",
url = "http://www.sciencedirect.com/science/article/pii/S004578251000201X",
author = "M. Braack and F. Schieweck",
keywords = "Porous media flow",
keywords = "Darcy-Brinkman equations",
keywords = "Stokes",
keywords = "Equal-order finite elements",
keywords = "Local projection stabilization"
}

@article{PaigeSaunders1975,
author = {C.~C. Paige and M.~A. Saunders},
title = "{Solution of sparse indefinite systems of linear equations}",
journal = {SIAM J. Numerical Analysis},
vol = {12},
year = {1975},
pages = {617--629}
} 

@article {Burman2005,
author = {Burman, Erik and Hansbo, Peter},
title = "{Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem}",
journal = {Numerical Methods for Partial Differential Equations},
volume = {21},
number = {5},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1098-2426},
url = {http://dx.doi.org/10.1002/num.20076},
doi = {10.1002/num.20076},
pages = {986--997},
keywords = {Crouzeix-Raviart element, Darcy-Stokes problem, Galerkin approach},
year = {2005},
}

@article{Burman2007,
title = "{A unified stabilized method for Stokes' and Darcy's equations}",
journal = "Journal of Computational and Applied Mathematics",
volume = "198",
number = "1",
pages = "35 - 51",
year = "2007",
note = "",
issn = "0377-0427",
doi = "DOI: 10.1016/j.cam.2005.11.022",
url = "http://www.sciencedirect.com/science/article/pii/S0377042705007053",
author = "Erik Burman and Peter Hansbo",
keywords = "Stokes' equation",
keywords = "Darcy's equation",
keywords = "Stabilized methods",
keywords = "Finite element",
keywords = "Interior penalty method",
keywords = "Nitsche's method",
keywords = "Domain decomposition",
keywords = "Inf-sup condition"
}

@article{Correa2009,
title = "{A unified mixed formulation naturally coupling Stokes and Darcy flows}",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "198",
number = "33-36",
pages = "2710 - 2722",
year = "2009",
note = "",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2009.03.016",
url = "http://www.sciencedirect.com/science/article/pii/S0045782509001340",
author = "M.R. Correa and A.F.D. Loula",
keywords = "Stabilized finite element",
keywords = "Stokes-Darcy flow",
keywords = "Beavers-Joseph interface condition",
keywords = "Galerkin least squares",
keywords = "Taylor-Hood elements"
}

@article{Dangelo2009,
title = "{A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows}",
publisher = {SIAM},
year = {2009},
doi = {DOI:10.1137/080726318},
issn = {00361429},
eissn = {10957170},
coden = {SJNAAM},
volume = {47},
number = {5},
pages = {3990-4020},
author = {Carlo D'Angelo and Paolo Zunino},
keywords = {generalized Stokes problem; Darcy problem; discontinuous coefficients; finite element approximation; interior penalty; iterative splitting methods; 76D07; 76S05; 35R05; 74S05; 65Y05; },
url = {http://dx.doi.org/doi/10.1137/080726318},
}

@article{Mardal2002,
 author = {Mardal, Kent Andre and Tai, Xue-Cheng and Winther, Ragnar},
 title = "{A Robust Finite Element Method for  Darcy--Stokes Flow}",
 journal = {SIAM J. Numer. Anal.},
 volume = {40},
 issue = {5},
 month = {May},
 year = {2002},
 issn = {0036-1429},
 pages = {1605--1631},
 numpages = {27},
 url = {http://dx.doi.org/10.1137/S0036142901383910},
 doi = {http://dx.doi.org/10.1137/S0036142901383910},
 acmid = {588593},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA},
 keywords = {Darcy--Stokes flow, nonconforming finite elements, singular perturbation problems, uniform error estimates},
} 

@article {Mardal2009,
author = {Karper, Trygve and Mardal, Kent-Andre and Winther, Ragnar},
title = "{Unified finite element discretizations of coupled Darcy-Stokes flow}",
journal = {Numerical Methods for Partial Differential Equations},
volume = {25},
number = {2},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1098-2426},
url = {http://dx.doi.org/10.1002/num.20349},
doi = {10.1002/num.20349},
pages = {311--326},
keywords = {coupled Darcy-Stokes flow, alternative weak formulations, nonconforming finite elements},
year = {2009},
}

@Article{Xie2008,
  author = 	 {Xie, X.P. and  Xu, J.C. and Xue, G.R },
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  journal = 	 {J. Comput. Math. },
  year = 	 {2008},
  OPTkey = 	 {},
  OPTvolume = 	 {26},
  OPTnumber = 	 {},
  OPTpages = 	 {437-455. },
  OPTmonth = 	 {},
  OPTnote = 	 {},
  OPTannote = 	 {}
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@Article{lashuk_vassilevski_nlaa_2011,
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@book{Girault-Raviart,
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@article {Nedelec1980,
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   pages = {315-341},
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   year = {1980}
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@article {Nedelec1986,
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   journal = {Numerische Mathematik},
   publisher = {Springer Berlin / Heidelberg},
   issn = {0029-599X},
   keyword = {Mathematics and Statistics},
   pages = {57-81},
   volume = {50},
   issue = {1},
   url = {http://dx.doi.org/10.1007/BF01389668},
   note = {10.1007/BF01389668},
   year = {1986}
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@article{Raviart1977,
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    posted-at = {2010-02-15 16:42:47},
    priority = {0},
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@article{Kolev09,
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 title = "{Parallel Auxiliary Space AMG for {H}(curl) Problems}",
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 volume = {27}, 
 year = {2009}
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@MISC{Kolev11,
 author = {Tzanio Kolev and Panayot~S. Vassilevski},
 title = "{Parallel Auxiliary Space AMG Solver for {H}(div) Problems}",
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 year = {December 15, 2011},
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@book{VassilevskiBook,
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 title = "{Multilevel Block Factorization Preconditioners}",
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@article {Mardal2011,
author = {Mardal, Kent-Andre and Winther, Ragnar},
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{metis,
author = {George Karypis and Vipin Kumar},
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, Panayot S. and Villa, Umberto},
title = "{A mixed formulation for the Brinkman problem}",
howpublished = {in preparation},
year = {2012},
organization = {Lawrence Livermore National Laboratory}
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@article{Benzi2006,
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collaboration = {},
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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}
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@book{Fortin83,
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                      Dunod, 1982",
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@article {Allaire91A,
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@article {Allaire91B,
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@INPROCEEDINGS{hypre_paper,
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    pages = {106--116},
    publisher = {SIAM}
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@misc{hypre,
key        = {hypre},
title      = "\hypre{}: High Performance Preconditioners",
note       = "{http://www.llnl.gov/CASC/hypre/}"
}

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     volume = {19},
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     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},
    }




%MARTAS
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doi = {10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y},
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@Book{quarteroni_numerical_models,
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   title       = {Numerical Models for Differential Problems},
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@MISC{hinze0,
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@article{silvester,
title = "Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow",
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number = "1-2",
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year = "2001",
note = "",
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url = "http://www.sciencedirect.com/science/article/B6TYH-42DP215-B/2/8d1c4398bf97800633a0d8b55d8bc920",
author = "D. Silvester and H. Elman and D. Kay and A. Wathen",
keywords = "Navier-Stokes equations",
keywords = "Incompressible flow",
keywords = "Preconditioning",
keywords = "Multigrid iteration"
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@article{kay,
 author = {D. Kay and D. Loghin and A. Wathen},
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} 

@article {ulbrich,
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keywords = {optimal flow control, compressible Navier–Stokes equations, gradient computation},
year = {2002},
}

@article {hinze1,
author = {Hinze, M. and Kunisch, K.},
title = {Second order methods for boundary control of the instationary Navier-Stokes system},
journal = {ZAMM - Journal of Applied Mathematics and Mechanics},
volume = {84},
number = {3},
publisher = {WILEY-VCH Verlag},
issn = {1521-4001},
url = {http://dx.doi.org/10.1002/zamm.200310094},
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pages = {171--187},
keywords = {time dependent Navier-Stokes equations, optimal boundary control, second order sufficient conditions, Newton's method},
year = {2004},
}

@Article{ gunzburger1991analysis-1,
	title = "{Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls}",
	author = "M.D. Gunzburger and L.S. Hou and T.P. Svobodny",
	journal = "Mod{\'e}lisation math{\'e}matique et analyse num{\'e}rique",
	volume = "25",
	number = "6",
	pages = "711--748",
	issn = "0764-583X",
	year = "1991",
	publisher = "EDP Sciences"
}

@Article{ gunzburger1991analysis,
	title = "{Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls}",
	author = "M.D. Gunzburger and S.L. Hou and T.P. Svobodny",
	journal = "Mathematics of Computation",
	volume = "57",
	number = "195",
	pages = "123--151",
	issn = "0025-5718",
	year = "1991",
	publisher = "JSTOR"
}

@article{cotter,
    author = {Cotter, S. L. and Dashti, M. and Robinson, J. C. and Stuart, A. M.},
    doi = {10.1088/0266-5611/25/11/115008},
    journal = {Inverse Problems},
    keywords = {bayes, parid},
    number = {11},
    pages = {115008+},
    posted-at = {2009-11-10 10:10:55},
    priority = {2},
    title = {{Bayesian inverse problems for functions and applications to fluid mechanics}},
    url = {http://dx.doi.org/10.1088/0266-5611/25/11/115008},
    volume = {25},
    year = {2009}
}


@Article{ gunzburger1999sensitivities,
	title = "{Sensitivities, adjoints and flow optimization}",
	author = "M.D. Gunzburger",
	journal = "International Journal for Numerical Methods in Fluids",
	volume = "31",
	number = "1",
	pages = "53--78",
	issn = "1097-0363",
	year = "1999",
	publisher = "John Wiley \& Sons"
}

@Techreport{bertoglio,
    author = {C. Bertoglio and P. Moireau and J. F. Gerbeau},
    title = {Sequential parameter estimation for fluid-structure problems. Application to hemodynamics},
    number = {7657},
    year = {2011},
    url = {http://hal.inria.fr/docs/00/60/33/99/PDF/RR-7657.pdf},
}

@Unpublished{md_av_uq,
    author = {M. D'Elia and A. Veneziani},
    title = {Uncertainty quantification for data assimilation in hemodynamics},
    year = {2011},
    note = {In preparation}
}

@Unpublished{md_eh_lh,
    author = {M. D'Elia and E. Haber and L. Horesh},
    title = {Design of Proper Orthogonal Decomposition basis by means of nonlinear inversion},
    year = {2011},
    note = {In preparation}
}

@Article{brummer,
AUTHOR = {P.M. den Reijer and D. Sallee and P. van der Velden and E. Zaaijer and W.J. Parks and S. Ramamurthy and T. Robbie and G. Donati C. and Lamphier and R. Beekman and M. Brummer},
TITLE = {Hemodynamic predictors of aortic dilatation in bicuspid aortic valve by velocity-encoded cardiovascular magnetic resonance},
JOURNAL = {Journal of Cardiovascular Magnetic Resonance},
VOLUME = {12},
YEAR = {2010},
NUMBER = {1},
PAGES = {4},
URL = {http://www.jcmr-online.com/content/12/1/4},
DOI = {10.1186/1532-429X-12-4},
PubMedID = {20070904},
ISSN = {1532-429X}
}

@book{RRGT,
 author               = {Galdi, G.P. and Rannacher, R. and Robertson, A.M. and Turek, S.},
 publisher            = {Birkhauser},
 title                = {{Hemodynamical Flows, Modeling, Analysis and Simulation}},
 year                 = {2008},
 }


@book{gunzburgerLSFEM,
 author               = {M. D. Gunzburger and P. B. Bochev},
 publisher            = {Springer},
 title                = {Least-Squares Finite Element Methods},
 year                 = {2009},
 }

@article{Tay2,
 author               = {Taylor, C. A. and Draney, M.T.},
 journal              = {Ann Rev Fluid Mech},
 pages                = {197-231},
 title                = {{Experimental and Computational Methods in Cardiovascular Fluid Mechanics}},
 volume               = {36},
 year                 = {2004},
 }

@article{Tay1,
 author               = {Taylor, C. A. and T. J. R. Hughes and C. K. Zarins},
 journal              = {Comput. Methods Appl. Mech. Eng.},
 pages                = {155-196},
 title                = {Finite element modeling of blood flow in arteries},
 volume               = {158},
 year                 = {1998},
 }

@article{taylor.eal:predictive,
 author               = {C.A. Taylor and M.T. Draney and J.P. Ku and D. Parker and B.N. Steele and K. Wang and C.K. Zarins},
 journal              = {Computer Aided Surgery},
 number               = {5},
 pages                = {231-247},
 title                = {Predictive medicine: Computational techniques in therapeutic decision-making},
 volume               = {4},
 year                 = {1999},
 }

@article{Benzi2005,
  author = {M. Benzi and G. H. Golub and J. Liesen},
  title = {{Numerical solution of saddle point problems}},
  journal = {Acta Numerica},
  year = {2005},
  volume = {14},
  pages = {1--137},
  owner = {uvilla},
  timestamp = {2011.05.31}
}


@article{gervasio2008convergence,
  author = {P. Gervasio},
  title = {{Convergence analysis of high order algebraic fractional step schemes
        for time-dependent Stokes equations}},
  journal = {SIAM Journal on Numerical Analysis},
  year = {2008},
  volume = {46},
  pages = {1682--1703},
  number = {4}
}

@article{gervasio2006algebraic,
  author = {P. Gervasio and F. Saleri and A. Veneziani},
  title = {{Algebraic fractional-step schemes with spectral methods for the
        incompressible Navier-Stokes equations}},
  journal = {Journal of Computational Physics},
  year = {2006},
  volume = {214},
  pages = {347--365},
  number = {1},
  issn = {0021-9991},
  publisher = {Elsevier}
}

@article{Perot93,
title = {An Analysis of the Fractional Step Method},
journal = {Journal of Computational Physics},
volume = {108"},
number = {1},
pages = {51 - 58},
year = {1993},
note = {},
issn = {0021-9991},
author = {J. B. Perot}
}

@Article{cachab,
author = {J Cahouet and J. P. Chabard },
title = {Some fast 3D finite element solvers for the generalized Stokes problem},
journal = {International Journal for Numerical Methods in Fluids},
year = {1988}
}

@article{quarteroni1999analysis,
  author = {A. Quarteroni and F. Saleri and A. Veneziani},
  title = {{Analysis of the Yosida method for the incompressible Navier-Stokes
        equations* 1}},
  journal = {Journal des Math{\'e}matiques Pures et Appliqu{\'e}s},
  year = {1999},
  volume = {78},
  pages = {473--503},
  number = {5},
  issn = {0021-7824},
  owner = {uvilla},
  publisher = {Elsevier},
  timestamp = {2011.05.31}
}

@ARTICLE{saleri2006pressure,
  author = {F. Saleri and A. Veneziani},
  title = {{Pressure correction algebraic splitting methods for the incompressible
        Navier-Stokes equations}},
  journal = {SIAM journal on numerical analysis},
  year = {2006},
  volume = {43},
  pages = {174--194},
  number = {1},
  issn = {0036-1429},
  owner = {uvilla},
  publisher = {[Philadelphia, Pa.]: The Society.},
  timestamp = {2011.05.31}
}

@ARTICLE{veneziani2003block,
  author = {A. Veneziani},
  title = {{Block factorized preconditioners for high-order accurate in time
	approximation of the Navier-Stokes equations}},
  journal = {Numerical Methods for Partial Differential Equations},
  year = {2003},
  volume = {19},
  pages = {487--510},
  number = {4},
  issn = {1098-2426},
  owner = {uvilla},
  publisher = {Wiley Online Library},
  timestamp = {2011.05.31}
}

@Unpublished{VeVi1,
 author = {A. Veneziani and U. Villa},
 title = {ALADINS: an ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations},
 note = {in preparation},
 year = {2011}
}

@Unpublished{VeVi2,
 author = {A. Veneziani and U. Villa},
 title = {On the solution of the discrete Laplace finite element pressure operator with direct methods},
 note = {in preparation},
 year = {2011}
}


@book{Complex,
 author               = {A. Quarteroni and L. Formaggia and A. Veneziani},
 editor               = {L. Formaggia and A. Quarteroni and A. Veneziani},
 publisher            = {Springer},
 title                = {Complex systems in Biomedicine},
 year                 = {2006},
 }


@Article{benzi_prec_2010,
author = {M. Benzi and M. A. Olshanskii and Z. Wang},
title = {Modified augmented Lagrangian preconditioners for the incompressible Navier-Stokes equations},
journal = {International Journal for Numerical Methods in Fluids},
volume = {66},
number = {4},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0363},
url = {http://dx.doi.org/10.1002/fld.2267},
doi = {10.1002/fld.2267},
pages = {486-508},
keywords = {preconditioning, saddle-point problems, Oseen problem, augmented Lagrangian method, Krylov subspace methods, parallel computing},
year = {2011},
}

@article{md_av1,
	title = {Methods for assimilating blood velocity measures in hemodynamics simulations: Preliminary results},
	volume = {1},
	issn = {1877-0509},
	shorttitle = {Methods for assimilating blood velocity measures in hemodynamics simulations},
	url = {http://www.sciencedirect.com/science/article/B9865-506HM1Y-4V/2/2dc72207b0901d405206de6c3a6e7373},
	doi = {10.1016/j.procs.2010.04.137},
	number = {1},
	journal = {Procedia Computer Science},
	author = {M. D'Elia and A. Veneziani},
	month = may,
	year = {2010},
	keywords = {Computational fluid dynamics, Data assimilation techniques, Hemodynamics, Inverse problems, Optimization techniques},
	pages = {1225--1233}
}

@misc{brummer,
	title = {Systolic Flow Jet Is An Indicator of Aortic Root Dilation for Bicuspid Aortic Valves},
	author = {P. van der Velden and D. Sallee and E. Zaaijer and W. J. Parks and S. Ramamurthy and T. Q. Robbie and J. Huckaby and S. Chochua and M. E. Brummer},
	year = {2008}
},

@techreport{head_estimation_1999,
	address = {Greenbelt, Maryland},
	type = {Internal Report from {DAO}},
	title = {Estimation Theory and Foundations of Atmospheric Data Assimilation},
	url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.6279},
	author = {R. A. Head and R. Todling},
	month = jun,
	year = {1999}
},


@article{md_av2,
	journal = {Proceedings of V  European Conference on Computational Fluid Dynamics, ECCOMAS},
	title = {A Data Assimilation technique for including noisy measurements of the velocity field into Navier-Stokes simulations},
	author = {M. D'Elia and A. Veneziani},
	month = jun,
	year = {2010}
},

@article{md_av3,
	journal = {Journal of Scientific Computing},
	title = {A Variational Data Assimilation Procedure for the Incompressible Navier-Stokes Equations in Hemodynamics},
	author = {M. D'Elia and M. Perego and A. Veneziani},
	doi = {10.1007/s10915-011-9547-6},
	year = {2011}
},


@book{bayes_choice,
    author = {R. P. Christian},
    edition = {2nd},
    howpublished = {Paperback},
    isbn = {0387715983},
    keywords = {bayes-minimax-dual, bayesian, decision\_theory, jeffreys\_prior, minimax, priors, textbook},
    month = jun,
    posted-at = {2010-05-05 14:49:36},
    priority = {2},
    publisher = {Springer Verlag, New York},
    series = {Springer Texts in Statistics},
    title = {{The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation}},
    url = {http://www.amazon.com/exec/obidos/redirect?tag=citeulike07-20\&path=ASIN/0387715983},
    year = {2007}
}




@Book{cardiov,
 title = {Cardiovascular Mathematics},
 publisher = {Springer},
 year = {2009},
 editor = {L. Formaggia and A. Quarteroni and A. Veneziani},
}


@INPROCEEDINGS{UKF2,
    author = {S. Julier and J. Uhlmann and H. Durrant-Whyte},
    title = {A new approach for filtering nonlinear systems},
    booktitle = {},
    journal = {American control conference},
    year = {1995},
    pages = {1628--1632}
}


@INPROCEEDINGS{UKF1,
    author = {S. J. Julier and J. K. Uhlmann},
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    booktitle = {},
    year = {1997},
    pages = {182--193}
}

 
@article{ROUKF,
	title = {Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems.},
	volume = {17},
	journal = {ESAIM: Control, Optimisation and Calculus of Variations},
	author = { P. Moireau and D. Chapelle},
	year = {2011},
	keywords = {electromechanical,fem,heart},
	pages = {380-405}
},


@article{sermesant_cardiac_2006,
	title = {Cardiac function estimation from {MRI} using a heart model and data assimilation: advances and difficulties.},
	volume = {10},
	issn = {1361-8415},
	url = {http://dx.doi.org/10.1016/j.media.2006.04.002},
	number = {4},
	journal = {Med Image Anal},
	author = {M. Sermesant and P. Moireau and O. Camara and J. {Sainte-Marie} and R. Andriantsimiavona and R. Cimrman and {DL} Hill and D. Chapelle and R. Razavi},
	year = {2006},
	keywords = {electromechanical,fem,heart},
	pages = {656, 642}
},

@article{haber_optimization_2000,
	title = {On optimization techniques for solving nonlinear inverse problems},
	volume = {16},
	issn = {0266-5611},
	url = {http://www.iop.org/EJ/abstract/0266-5611/16/5/309},
	number = {5},
	journal = {Inverse Problems},
	author = {E. Haber and U. M. Ascher and D. Oldenburg},
	year = {2000},
	pages = {1263--1280}
},

@techreport{edge2004,
    HAL_ID = {inria-00070653},
    URL = {http://hal.inria.fr/inria-00070653/en/},
    title = { {E}dge {S}tabilization for the {I}ncompressible {N}avier-{S}tokes {E}quations: a {C}ontinuous {I}nterior {P}enalty {F}inite {E}lement {M}ethod},
    author = {E. Burman and M. A. Fern{\'a}ndez and P. Hansbo},
    keywords = {{OSEEN} {EQUATION} / {INTERIOR} {PENALTY} / {GRADIENT} {JUMP} / {MINIMAL} {STABILIZED} {METHOD}},
    language = {{E}nglish},
    affiliation = {{REO} - {INRIA} {R}ocquencourt - {INRIA} - {L}aboratoire {J}acques-{L}ouis {L}ions },
    pages = {34 },
    type = {{R}esearch {R}eport},
    institution = {INRIA},
    number = {{RR}-5349},
    year = {2004},
    URL = {http://hal.inria.fr/inria-00070653/PDF/RR-5349.pdf},
},

﻿
@book{rivlin2003,
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	pages = {166}
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@book{quarteroni_numerical_1994,
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@book{qss,
	title = { Numerical mathematics},
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       pages = {654}
},

@article {nudging,
author = {Davies, H. C. and Turner, R. E.},
title = {Updating prediction models by dynamical relaxation: an examination of the technique},
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volume = {103},
number = {436},
publisher = {John Wiley & Sons, Ltd},
issn = {1477-870X},
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pages = {225--245},
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}

@article{burman_edge_2006,
	title = {Edge stabilization for the generalized Stokes problem: A continuous interior penalty method},
	volume = {195},
	issn = {0045-7825},
	url = {http://www.sciencedirect.com/science/article/B6V29-4GNKR8G-1/2/20d8a273b6719bbb292138494f7e2a95},
	doi = {10.1016/j.cma.2005.05.009},
	abstract = {
In this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher order version of the {Brezzi-Pitkäranta} penalty stabilization {[F.} Brezzi, J. Pitkäranta, On the stabilization of finite element approximations of the Stokes equations, in: W. Hackbusch {(Ed.),} Efficient Solution of Elliptic Systems, Vieweg, 1984], but gives better resolution on the boundary for the Stokes equation than does classical Galerkin least-squares formulation. We prove optimal and quasi-optimal convergence properties for Stokes' problem and for the porous media models of Darcy and Brinkman. Some numerical examples are given.},
	number = {19-22},
	journal = {Computer Methods in Applied Mechanics and Engineering},
	author = {E. Burman and P. Hansbo},
	month = apr,
	year = {2006},
	keywords = {Finite {element,Generalized} Stokes' {equation,Gradient} {jumps,Inf-sup} {condition,Interior} penalty {method,Stabilized} methods},
	pages = {2393--2410}
},

@article{womersley,
    author = {Womersley, J. R.},
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    journal = {The Journal of physiology},
    keywords = {womersley},
    month = mar,
    number = {3},
    pages = {553--563},
    pmid = {14368548},
    posted-at = {2010-08-26 16:41:59},
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    title = {{Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known.}},
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    volume = {127},
    year = {1955}
}


@book{gunzburger_perspectives_2002,
	title = {Perspectives in Flow Control and Optimization},
	isbn = {{089871527X}},
	publisher = {Society for Industrial Mathematics},
	author = {M. D. Gunzburger},
	month = dec,
	year = {2002}
},

@misc{carr_basic_2008,
	address = {University of Oklahoma},
	type = {Lecture Notes},
	title = {Basic concepts of data assimilation},
	author = {F. Carr and M. Xue},
	year = {2008}
},

@unpublished{bouttier_data_1999,
	title = {Data Assimilation Concepts and Methods},
	author = {F. Bouttier and P. Courtier},
	year = {1999},
	note = {Meteorological Training Course Lecture Series, {ECMWF}}
},

@Article{VV,
	author = {A. Veneziani and C. Vergara},
	pages = {1685-1700},
	volume = {196},
	year = {2007},
	journal = {Comp Meth Appl Mech Engr},
	title = {{An approximate method for
  solving incompressible Navier-Stokes problem with flow rate conditions}},
	number = {9-12}
}

@article{burman_edge_2006,
 author               = {E. Burman and P. Hansbo},
 doi                  = {10.1016/j.cma.2005.05.009},
 issn                 = {0045-7825},
 journal              = {Computer Methods in Applied Mechanics and Engineering},
 keywords             = {Finite {element,Generalized} Stokes' {equation,Gradient} {jumps,Inf-sup} {condition,Interior} penalty {method,Stabilized} methods},
 month                = {apr},
 number               = {19-22},
 pages                = {2393--2410},
 title                = {Edge stabilization for the generalized Stokes problem: A continuous interior penalty method},
 url                  = {http://www.sciencedirect.com/science/article/B6V29-4GNKR8G-1/2/20d8a273b6719bbb292138494f7e2a95},
 volume               = {195},
 year                 = {2006},
 }

@article{wang_data_2000,
	title = {Data assimilation and its applications},
	volume = {97},
	url = {http://www.pnas.org/content/97/21/11143.abstract},
	doi = {{VL}  - 97},
	number = {21},
	journal = {Proceedings of the National Academy of Sciences of the United States of America},
	author = {B. Wang and X. Zou and J. Zhu},
	month = oct,
	year = {2000},
	pages = {11143--11144}
},

@article{lundvall__2006,
	title = { Iterative methods for data assimilation for Burgers' equation },
	volume = { 14 },
	number = { 5 },
	journal = { Journal of inverse and ill-posed problems },
	author = {J. Lundvall and V. Kozlov and P. Weinerfelt},
	year = {2006},
	pages = { 505--535 }
},

@techreport{robinson_over_2000,
	address = {Cambridge, Massachusetts},
	title = {Over View of Data Assimilation},
	number = {62},
	institution = {Harvard University},
	author = {A. R. Robinson and P. {F.J.} Lermusiaux},
	month = aug,
	year = {2000}
},

@article{Veneziani20071685,
title = "An approximate method for solving incompressible Navier-Stokes problems with flow rate conditions",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "196",
number = "9-12",
pages = "1685 - 1700",
year = "2007",
note = "",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2006.09.011",
url = "http://www.sciencedirect.com/science/article/B6V29-4MCW9MT-1/2/c794dcb6534ace37ab5d25a1843f5c13",
author = "A. Veneziani and C. Vergara",
keywords = "Incompressible fluids",
keywords = "Flow rate boundary conditions",
keywords = "Lagrange multipliers"
},

@phdthesis{veneziani_phd,
	author = {A. Veneziani}, 
	title = {Mathematical and numerical modeling of blood flow problems}, 
	school = {Politecnico di Milano}, 
	year = {1998}
},

@article{ide_unified_1997,
	title = {Unified Notation for Data Assimilation: Operational, Sequential and Variational},
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@misc{carr_kalman_2008,
	address = {University of Oklahoma},
	type = {Lecture Notes},
	title = {Kalman Filter},
	author = {F. Carr and M. Xue},
	year = {2008}
},

@article{formaggia_new_2008,
	title = {A New Approach to Numerical Solution of Defective Boundary Value Problems in Incompressible Fluid Dynamics},
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	url = {http://portal.acm.org/citation.cfm?id=1461678.1461679&coll=GUIDE&dl=GUIDE},
	number = {6},
	journal = {{SIAM} J. Numer. Anal.},
	author = {L. Formaggia and A. Veneziani and C. Vergara},
	year = {2008},
	keywords = {computational hemodynamics,flow rate boundary condition,mean pressure boundary condition,navier-stokes equations},
	pages = {2769--2794}
},

@book{Hansen,
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@Article{LionsPNAS,
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@Book{Comincioli,
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@ARTICLE{simoncini,
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@book{elman_finite_2005,
	title = {Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics},
	author = {H. C. Elman and D. J. Silvester and A. J. Wathen},
	year = {2005},
	publisher = {Oxford Science Publications},
	keywords = {65 Numerical analysis}
}


@TECHREPORT{iteration_accuracy,
author = {X. Du and E. Haber and M. Karampataki and D. B. Szyld},
  title = {Varying Iteration Accuracy Using Inexact Conjugate Gradients
          in Control Problems governed by {PDE}'s},
  institution = {Department of Mathematics, Temple University},
  number = {08-06-27},
  year = {2008},
  month = {JUN}
}

@article{podNewlook,
     jstor_articletype = {research-article},
     title = {A New Look at Proper Orthogonal Decomposition},
     author = {M. Rathinam and L. R. Petzold},
     journal = {SIAM Journal on Numerical Analysis},
     jstor_issuetitle = {},
     volume = {41},
     number = {5},
     jstor_formatteddate = {2004},
     pages = {pp. 1893-1925},
     ISSN = {00361429},
     year = {2004},
     publisher = {Society for Industrial and Applied Mathematics},
     copyright = {Copyright 2004 Society for Industrial and Applied Mathematics},
    }
    
    
    
@article {gmresr,
author = {Van der Vorst, H. A. and Vuik, C.},
title = {GMRESR: a family of nested GMRES methods},
journal = {Numerical Linear Algebra with Applications},
volume = {1},
number = {4},
publisher = {John Wiley & Sons, Ltd},
issn = {1099-1506},
url = {http://dx.doi.org/10.1002/nla.1680010404},
doi = {10.1002/nla.1680010404},
pages = {369--386},
keywords = {GMRES, Unsymmetric linear systems, Iterative solver},
year = {1994},
}

@article{fgmres_gmresr,
 author = {Vuik, C.},
 title = {New insights in GMRES-like methods with variable preconditioners},
 journal = {J. Comput. Appl. Math.},
 volume = {61},
 issue = {2},
 month = {July},
 year = {1995},
 issn = {0377-0427},
 pages = {189--204},
 numpages = {16},
 url = {http://dl.acm.org/citation.cfm?id=219222.219250},
 doi = {10.1016/0377-0427(94)00067-B},
 acmid = {219250},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 keywords = {FGMRES, GMRESR, iterative solver, nonsymmetric linear systems},
}

@article{podFluid1,
     jstor_articletype = {research-article},
     title = {Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics},
     author = {Kunisch, K. and Volkwein, S.},
     journal = {SIAM Journal on Numerical Analysis},
     volume = {40},
     number = {2},
     jstor_formatteddate = {2003},
     pages = {pp. 492-515},
     ISSN = {00361429},
     year = {2003},
     publisher = {Society for Industrial and Applied Mathematics},
     copyright = {Copyright 2003 Society for Industrial and Applied Mathematics},
    }
    
@article {podOpt,
   author = {M. Fahl and E. W. Sachs},
   affiliation = {Fachbereich IV — Mathematik, Universität Trier, D-54286 Trier, Germany},
   title = {Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition},
   booktitle = {Large-Scale PDE-Constrained Optimization},
   series = {Lecture Notes in Computational Science and Engineering},
   editor = {Biegler, Lorenz T. and Heinkenschloss, Matthias and Ghattas, Omar and Bloemen Waanders, Bart},
   publisher = {Springer Berlin Heidelberg},
   isbn = {978-3-642-55508-4},
   keyword = {Mathematics},
   pages = {268-280},
   volume = {30},
   year = {2003}
}

@Book{reducedBasis,
   address     = {Cambridge, MA, US},
   affiliation = {OTHER},
   author      = {A. T. Patera and G. Rozza},
   keywords    = {reduced basis methods; parametrized PDEs; Galerkin method; a posteriori error estimation; reduced order modelling},
   oai-id      = {oai:infoscience.epfl.ch:124801},
   publisher   = {MIT, Massachusetts Institute of Technology},
   series      = {MIT-Pappalardo Graduate Monographs in Mechanical Engineering},
   status      = {PUBLISHED},
   title       = {Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations},
   unit        = {CMCS},
   url         = {http://augustine.mit.edu/methodology/methodology_book.htm},
   year        = 2007
}

@ARTICLE{podWillcox,
    author = {K. Willcox and J. Peraire},
    title = {Balanced model reduction via the proper orthogonal decomposition},
    journal = {AIAA Journal},
    year = {2002},
    pages = {2323-2330}
}

@article {podFluid2,
author = {Ravindran, S. S.},
title = {A reduced-order approach for optimal control of fluids using proper orthogonal decomposition},
journal = {International Journal for Numerical Methods in Fluids},
volume = {34},
number = {5},
publisher = {John Wiley and Sons, Ltd.},
issn = {1097-0363},
pages = {425-448},
keywords = {flow control, Galerkin approximation, optimal control, POD, reduced-order model},
year = {2000}
}


@article{rozza,
title = "On the stability of the reduced basis method for Stokes equations in parametrized domains",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "196",
number = "7",
pages = "1244 - 1260",
year = "2007",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2006.09.005",
author = "G. Rozza and K. Veroy",
}

@article{Peterson,
 author = {J. S. Peterson},
 title = {The reduced basis method for incompressible viscous flow calculations},
 journal = {SIAM J. Sci. Stat. Comput.},
 volume = {10},
 issue = {4},
 month = {July},
 year = {1989},
 issn = {0196-5204},
 pages = {777-786},
 numpages = {10},
 doi = {10.1137/0910047},
 acmid = {64934},
 publisher = {Society for Industrial and Applied Mathematics},
 address = {Philadelphia, PA, USA}
} 



