References
- Bazilevs , Y. , Calo , V.M. , Zhang , Y. and Hughes , T.J.R. 2006 . Isogeometric fluid-structure interaction analysis with applications to arterial blood flow . Comput. Mech. , 38 : 310 – 322 .
- Quarteroni A, Crosetto P, Deparis S. Efficient solution of fluid-structure interaction problems in computational hemodynamics. Vol. 1281, Aip Conference Proceedings. American Institute of Physics: College Park, Maryland; 2010.
- Sanchez-Palencia , E. 1980 . Non-homogeneous media and vibration theory. Vol. 127, Lecture Notes in Physics , Berlin : Springer-Verlag .
- Sanchez-Palencia , E. and Ene , H.I. 1975 . Equations et phénomènes de surface pour l’écoulement dans un modèle de milieu poreux . J. Mécanique , 14 : 73 – 108 .
- Allaire , A. 1992 . Homogenization and two-scale convergence . SIAM J. Math. Anal. , 23 : 1482 – 1518 .
- Tartar , L. 1980 . Incompressible fluid flow in a porous medium – convergence of the homogenization process. Vol. 127, Lecture Notes in Physics , Berlin : Springer-Verlag .
- Biot , M.A. 1941 . General theory of three dimensional consolidation . J. Appl. Phys. , 12 : 155 – 164 .
- Burridge , R. and Keller , J.B. 1981 . Poroelasticity equations derived from microstructure . J. Acoust. Soc. Am. , 70 : 1140 – 1146 .
- Lee , C.K. and Mei , C.C. 1997 . Re-examination of the equations of poroelasticity . Int. J. Eng. Sci. , 35 : 329 – 352 .
- Temam , R. 1977 . Navier–Stokes equations: theory and numerical analysis , New York (NY) : Elsevier North-Holland .
- Gurtin , M.E. 1981 . An introduction to continuum mechanics , San Diego : Academics Press .
- Formaggia , L. , Quarteroni , A. and Veneziani , A. 2009 . Cardiovascular mathematics: modeling and simulation of the circulatory system. Modeling, Simulation, & Applications , Milan : Springer .
- Galdi , G.P. and Rannacher , R. 2010 . Fundamental trends in fluid-structure interaction. Vol. 1, Contemporary challenges in mathematical fluid dynamics and its applications , Singapore : World Scientific Publishing Company .
- Efendiev Y, Hou T, Ginting V. Multiscale finite element methods for nonlinear problems and their applications. Commun. Math. Sci. 2004:2:553–589.
- Popov P, Gorb Y, Efendiev Y. Iterative upscaling of flows in deformable porous media. 2013 (Under Review).
- Chechkin , G.A. , Piatniski , A.L. and Shamev , A.S. 2007 . Homogenization: methods and applications. Vol. 234, Translations of Mathematical Monographs , Providence (RI) : American Mathematical Society .
- Efendiev , Y. and Pankov , A. 2003 . Numerical homogenization of monotone elliptic operators . SIAM MMS , 2 : 62 – 79 .