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@Book{quarteroni_numerical_models,
   address     = {Heidelberg, DE},
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   author      = {A. Quarteroni},
   keywords    = {Analysis; Numerical modelling; PDE},
   oai-id      = {oai:infoscience.epfl.ch:140685},
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@Article{heys2010,
	title = "{Weighted least-squares finite elements based on particle imaging velocimetry data}",
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title = "Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow",
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keywords = "Preconditioning",
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keywords = {optimal flow control, compressible Navier–Stokes equations, gradient computation},
year = {2002},
}

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@Article{ gunzburger1991analysis-1,
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    posted-at = {2009-11-10 10:10:55},
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@Unpublished{md_av_uq,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@Unpublished{md_eh_lh,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},
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    note = {In preparation}
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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,
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@book{gunzburgerLSFEM,
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@article{taylor.eal:predictive,
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@article{gauthier2004fast,
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@article{gervasio2006algebraic,
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@article{quarteroni1999analysis,
  author = {A. Quarteroni and F. Saleri and A. Veneziani},
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        equations* 1}},
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  year = {1999},
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}

@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},
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  owner = {uvilla},
  publisher = {[Philadelphia, Pa.]: The Society.},
  timestamp = {2011.05.31}
}

@article{veneziani2003block,
  author = {A. Veneziani},
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  pages = {487--510},
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  owner = {uvilla},
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  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},
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 year = {2011}
}


@book{Complex,
 author               = {A. Quarteroni and L. Formaggia and A. Veneziani},
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 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}
},

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	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},
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    month = jun,
    posted-at = {2010-05-05 14:49:36},
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    publisher = {Springer Verlag, New York},
    series = {Springer Texts in Statistics},
    title = {{The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation}},
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    year = {2007}
}




@Book{cardiov,
 title = {Cardiovascular Mathematics},
 publisher = {Springer},
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@INPROCEEDINGS{UKF2,
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@INPROCEEDINGS{UKF1,
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@article{sermesant_cardiac_2006,
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@article{haber_optimization_2000,
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@techreport{edge2004,
    HAL_ID = {inria-00070653},
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    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},
},

﻿
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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.},
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@misc{carr_basic_2008,
	address = {University of Oklahoma},
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@unpublished{bouttier_data_1999,
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@Article{VV,
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@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},
 }

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@techreport{robinson_over_2000,
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	year = {2000}
},

@article{Veneziani20071685,
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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,
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	year = {1998}
},

@article{ide_unified_1997,
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@misc{carr_kalman_2008,
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@article{formaggia_new_2008,
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@ARTICLE{simoncini,
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@TECHREPORT{iteration_accuracy,
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@article{podFluid1,
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@article {podOpt,
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@Book{reducedBasis,
   address     = {Cambridge, MA, US},
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   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},
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}

@ARTICLE{podWillcox,
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@article {podFluid2,
author = {Ravindran, S. S.},
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keywords = {flow control, Galerkin approximation, optimal control, POD, reduced-order model},
year = {2000}
}


@article{rozza,
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} 



