D. Amsallem and C. Farhat, Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity, AIAA Journal, vol.46, issue.7, 2008.
DOI : 10.2514/1.35374

A. Astolfi, Model Reduction by Moment Matching for Linear and Nonlinear Systems, IEEE Transactions on Automatic Control, vol.55, issue.10, pp.2321-2336, 2010.
DOI : 10.1109/TAC.2010.2046044

K. J. Bathe, Finite Element Procedures, 1996.

R. Chabiniok, D. Chapelle, P. Lesault, A. Rahmouni, and J. Deux, Validation of a biomechanical heart model using animal data with acute myocardial infarction, MICCAI Workshop on Cardiovascular Interventional Imaging and Biophysical Modelling (CI2BM09), 2009.
URL : https://hal.archives-ouvertes.fr/inria-00418373

P. G. Ciarlet, The Finite Element Method for Elliptic Problems, 1987.

P. Clément, Approximation by finite element functions using local regularization, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.9, issue.R2, pp.77-84, 1975.
DOI : 10.1051/m2an/197509R200771

L. Daniel, C. S. Ong, L. S. Chay, H. L. Kwok, and J. White, A multiparameter momentmatching model-reduction approach for generating geometrically parameterized interconnect performance models. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on Automatic Control, vol.23, issue.5, pp.678-693, 2004.

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, 1992.

B. F. Feeny and R. Kappagantu, ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS, Journal of Sound and Vibration, vol.211, issue.4, pp.607-616, 1998.
DOI : 10.1006/jsvi.1997.1386

T. M. Flett, Differential Analysis, 1980.
DOI : 10.1017/CBO9780511897191

S. Gugercin and A. C. Athanasios, A Survey of Model Reduction by Balanced Truncation and Some New Results, International Journal of Control, vol.26, issue.8, pp.77748-766, 2004.
DOI : 10.1002/(SICI)1099-1239(199903)9:3<183::AID-RNC399>3.0.CO;2-E

M. Hinze and S. Volkwein, Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control, Dimension Reduction of Large-Scale Systems, pp.261-306, 2005.
DOI : 10.1007/3-540-27909-1_10

M. Hinze and S. Volkwein, Error estimates for abstract linear???quadratic optimal control problems using proper orthogonal decomposition, Computational Optimization and Applications, vol.40, issue.3, pp.319-345, 2008.
DOI : 10.1007/s10589-007-9058-4

P. Holmes, J. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 1996.
DOI : 10.1017/cbo9780511622700

M. Kahlbacher and S. Volkwein, Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems, Discussiones Mathematicae. Differential Inclusions, Control and Optimization, vol.27, issue.1, pp.95-117, 2007.
DOI : 10.7151/dmdico.1078

D. Kosambi, Statistics in Function Space, J. Indian Math. Soc. (N.S.), vol.7, pp.76-88, 1943.
DOI : 10.1007/978-81-322-3676-4_15

K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for parabolic problems, Numerische Mathematik, vol.90, issue.1, pp.117-148, 2001.
DOI : 10.1007/s002110100282

K. Kunisch and S. Volkwein, Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.40, issue.2, pp.492-515, 2002.
DOI : 10.1137/S0036142900382612

K. Kunisch and S. Volkwein, Proper orthogonal decomposition for optimality systems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.42, issue.1, pp.1-23, 2008.
DOI : 10.1051/m2an:2007054

Y. Maday, A. T. Patera, and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations, Journal of Scientific Computing, vol.17, issue.1/4, pp.437-446, 2002.
DOI : 10.1023/A:1015145924517

URL : https://hal.archives-ouvertes.fr/hal-00798389

C. Prud-'homme, D. V. Rovas, K. Veroy, and A. T. Patera, A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.5, pp.747-771, 2002.
DOI : 10.1051/m2an:2002035

URL : https://hal.archives-ouvertes.fr/hal-01220802

D. V. Rovas, L. Machiels, and Y. Maday, Reduced-basis output bound methods for parabolic problems, IMA Journal of Numerical Analysis, vol.26, issue.3, pp.423-445, 2006.
DOI : 10.1093/imanum/dri044

URL : https://hal.archives-ouvertes.fr/hal-00112600

G. Rozza, D. B. Huynh, and A. T. Patera, Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations, Archives of Computational Methods in Engineering, vol.40, issue.11, pp.229-275, 2008.
DOI : 10.1007/s11831-008-9019-9

J. Sainte-marie, D. Chapelle, R. Cimrman, and M. Sorine, Modeling and estimation of the cardiac electromechanical activity, Computers & Structures, vol.84, issue.28, pp.1743-1759, 2006.
DOI : 10.1016/j.compstruc.2006.05.003

URL : https://hal.archives-ouvertes.fr/hal-00839206

T. Stykel, Balanced truncation model reduction for semidiscretized Stokes equation. Linear Algebra and its Applications, pp.262-289, 2006.

K. Veroy, C. Prud-'homme, and A. T. Patera, Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds, Comptes Rendus Mathematique, vol.337, issue.9, pp.619-624, 2003.
DOI : 10.1016/j.crma.2003.09.023

URL : https://hal.archives-ouvertes.fr/hal-01219048

K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA Journal, pp.2323-2330, 2002.