Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction - Fluid-Structure Interaction and Biomedical Applications - page 473

10. P.B. Bochev, M.D. Gunzburger, Accuracy of least-squares methods for the Navier-Stokes
equations. Comput. Fluids 22 , 549-563 (1993)
11. P.B. Bochev, M.D. Gunzburger, Least-Squares Finite Element Methods (Springer, Berlin,

2009)
12. P.T. Boggs, J.W. Tolle, Sequential quadratic programming. Acta Numer. 4 , 1-51 (1995)
13. D. Calvetti, E. Somersalo, An Introduction to Bayesian Scientific Computing: Ten Lectures on
Subjective Computing . Surveys and Tutorials in the Applied Mathematical Sciences (Springer
Science+Business Media, New York, 2007)
14. I. Campbell, W. Robert Taylor, Flow and atherosclerosis, in Hemodynamics and Mechanobi-
ology of Endothelium (World Scientific, Hackensack, 2010)
15. D. Chapelle, A. Gariah, J. Sainte-Marie, Galerkin approximation with proper orthogonal
decomposition: new error estimates and illustrative examples. ESAIM: Math. Model. Numer.
Anal. 46 , 731-757 (2012)
16. M. D'Elia, A. Veneziani, Uncertainty quantification for data assimilation in a steady
incompressible navier-stokes problem. ESAIM: Math. Model. Numer. Anal. 47 , 1037-1057

(2013)
17. M. D'Elia, L. Mirabella, T. Passerini, M. Perego, M. Piccinelli, C. Vergara, A. Veneziani, Some
applications of variational data assimilation in computational hemodynamics, in Modelling of
Physiological Flows , ed. by D. Ambrosi, A. Quarteroni, G. Rozza. MS&A Series (Springer,
Berlin, 2011), pp. 363-394
18. M. D'Elia, M. Perego, A. Veneziani, A variational data assimilation procedure for the
incompressible navier stokes equations in hemodynamics. J. Sci. Comput. 52 (2), 340-359

(2012)
19. H. Delingette, M. Sermesant, R. Cabrera-Lozoya, C. Tobon-Gomez, P. Moireau, R.M. Figueras
i Ventura, K. Lekadir, A. Hernandez, M. Garreau, E. Donal, C. Leclercq, S.G. Duckett,
K. Rhode, C.A. Rinaldi, A.F. Frangi, R. Razavi, D. Chapelle, N. Ayache, S. Marchesseau,
Personalization of a cardiac electromechanical model using reduced order unscented kalman
filtering from regional volumes. Med. Image Anal. 17 , 816-829 (2013)
20. J. Donea, S. Giuliani, J.P. Halleux, An arbitrary lagrangian-eulerian finite element method for
transient dynamic fluid-structure interactions. Comput. Methods Appl. Mech. Eng. 33 (1-3),

689-723 (1982)
21. R.P. Dwight, Bayesian inference for data assimilation using least-squares finite element
methods, in IOP Conference Series: Materials Science and Engineering , vol. 10 (IOP
Publishing, Bristol, 2010), p. 012224
22. B. Einarsson, Accuracy and Reliability in Scientific Computing , vol. 18 (Society for Industrial
Mathematics, Philadelphia, 2005)
23. H.W. Engl, M. Hanke, A. Neubauer, Regularization of Inverse Problems . Mathematics and its
Applications (Springer, Berlin, 1996)
24. L. Formaggia, A. Veneziani, C. Vergara, A new approach to numerical solution of defective
boundary value problems in incompressible fluid dynamics. SIAM J. Numer. Anal. 46 (6),

2769-2794 (2008)
25. L. Formaggia, A. Quarteroni, A. Veneziani, Cardiovascular Mathematics: Modeling and
Simulation of the Circulatory System , vol. 1 (Springer, Berlin, 2009)
26. L. Formaggia, A. Veneziani, C. Vergara, Flow rate boundary problems for an incompressible
fluid in deformable domains: formulations and solution methods. Comput. Methods Appl.

Mech. Eng. 9 (12), 677-688 (2010)
27. P.C. Franzone, L.F. Pavarino, A Parallel Solver for Reaction-Diffusion Systems in Computa-
tional Electrocardiology, Math. Model. Methods in Appl. Sci. 14 (6), 883-911 (2004) doi: 10.
1142/s0218202504003489
28. B. Fristedt, N. Jain, N.V. Krylov, Filtering and Prediction: A Primer , STML vol. 38, AMS,
Providence, RI (2007)
29. K. Funamoto, T. Hayase, Reproduction of pressure field in ultrasonic-measurement-integrated
simulation of blood flow. Int. J. Numer. Methods Biomed. Eng. 29 (7), 726-740 (2013)