[53] C. D'Angelo and P. Zunino. Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport. *ESAIM: Mathematical Modelling and Numerical Analysis*, 45(3):447-476, May 2011.

[54] R. Dautray and J.-L. Lions. Evolution problems I, volume 5 of Mathematical analysis and numerical methods for science and technology, 1992.

[55] R. De Boer. *Trends in continuum mechanics of porous media*, volume 18. Springer Science & Business Media, 2005.

[56] M. Deville, R. Natalini, and C. Poignard. A continuum mechanics model of enzyme-based tissue degradation in cancer therapies. *Bulletin of mathematical biology*, 80(12):3184-3226, 2018.

[57] G. Duvaut and J. L. Lions. *Les inéquations en mécanique et en physique*. Dunod, 1972.

[58] A. Ern and J.-L. Guermond. *Finite Elements III: First-Order and Time-Dependent PDEs*, volume 74. Springer Nature, 2020.

[59] A. Ezziani. *Modélisation mathématique et numérique de la propagation d'ondes dans les milieux viscoélastiques et poroélastiques*. PhD thesis, ENSTA ParisTech, 2005.

[60] G. Fichera. Uniqueness, existence and estimate of the solution in the dynamical problem of thermo-diffusion in an elastic solid. *Archives of Mechanics*, 26(5):903-920, 1974.

[61] M. Genet, C. Patte, C. Fetita, P.-Y. Brillet, and D. Chapelle. Personalized pulmonary poromechanics. *Computer Methods in Biomechanics and Biomedical Engineering*, 23(sup1):S119-S120, 2020.

[62] L. Gil, M. Jabbour, and N. Triantafyllidis. The Role of the Relative Fluid Velocity in an Objective Continuum Theory of Finite Strain Poroelasticity. *Journal of Elasticity*, pages 1-46, 2022.

[63] V. Girault and P.-A. Raviart. *Finite element methods for Navier-Stokes equations: theory and algorithms*, volume 5. Springer Science & Business Media, 2012.

[64] L. Guo, J. C. Vardakis, T. Lassila, M. Mitolo, N. Ravikumar, D. Chou, M. Lange, A. Sarrami-Foroushani, B. J. Tully, Z. A. Taylor, S. Varma, A. Venneri, A. F. Frangi, and Y. Ventikos. Subject-specific multi-poroelastic model for exploring the risk factors associated with the early stages of Alzheimer's disease. *Interface Focus*, 8(1):20170019, Feb. 2018.

[65] U. Hornung, L. Kadanoff, J. E. Marsden, L. Sirovich, S. Wiggins, and F. John, editors. *Homogenization and Porous Media*, volume 6 of *Interdisciplinary Applied Mathematics*. Springer New York, New York, NY, 1997.

[66] J. M. Huyghe, T. Arts, D. H. van Campen, and R. S. Reneman. Porous medium finite element model of the beating left ventricle. *American Journal of Physiology-Heart and Circulatory Physiology*, 262(4):H1256-H1267, Apr. 1992.

[67] N. Koshiba, J. Ando, X. Chen, and T. Hisada. Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model. *Journal of biomechanical engineering*, 129(3):374-385, 2007.

[68] O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural'ceva. *Linear and quasi-linear equations of parabolic type*, volume 23. American Mathematical Soc., 1968.

[69] J. J. Lee. Robust three-field finite element methods for Biot's consolidation model in poroelasticity. *BIT Numerical Mathematics*, 58(2):347-372, June 2018.

[70] J. J. Lee, E. Piersanti, K.-A. Mardal, and M. E. Rognes. A mixed finite element method for nearly incompressible multiple-network poroelasticity. *SIAM Journal on Scientific Computing*, 41(2):A722-A747, 2019.
[71] J. L. Lions and E. Magenes. *Non-homogeneous boundary value problems and applications*, volume 1. Springer Science & Business Media, 1972.

[72] A. Logg, K.-A. Mardal, G. N. Wells, et al. *Automated Solution of Differential Equations by the Finite Element Method*. Springer, 2012.

[73] S. L. Lopatnikov and A. H. D. Cheng. Macroscopic Lagrangian formulation of poroelasticity with porosity dynamics. *Journal of the Mechanics and Physics of Solids*, 52(12):2801–2839, Dec. 2004.

[74] B. Markert, Y. Heider, and W. Ehlers. Comparison of monolithic and splitting solution schemes for dynamic porous media problems. *International Journal for Numerical Methods in Engineering*, 82(11):1341–1383, 2010.

[75] C. Michler, A. N. Cookson, R. Chabiniok, E. Hyde, J. Lee, M. Sinclair, T. Sochi, A. Goyal, G. Vigueras, D. A. Nordsletten, and N. P. Smith. A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model. *International Journal for Numerical Methods in Biomedical Engineering*, 29(2):217–232, 2013.

[76] A. Mikelić. *Homogenization Theory and Applications to Filtration through Porous Media*, volume 1734, pages 127–214. Springer Berlin Heidelberg, Berlin, Heidelberg, 2000.

[77] A. Mikelić and M. F. Wheeler. Convergence of iterative coupling for coupled flow and geomechanics. *Computational Geosciences*, 17(3):455–461, June 2013.

[78] M. A. Murad and J. H. Cushman. Multiscale flow and deformation in hydrophilic swelling porous media. *International Journal of Engineering Science*, 34(3):313–338, Feb. 1996.

[79] M. P. Nash and P. J. Hunter. Computational mechanics of the heart. *Journal of elasticity and the physical science of solids*, 61(1):113–141, 2000.

[80] S. Owczarek. A Galerkin method for Biot consolidation model. *Mathematics and mechanics of solids*, 15(1):42–56, 2010.

[81] R. Oyarzúa and R. Ruiz-Baier. Locking-Free Finite Element Methods for Poroelasticity. *SIAM Journal on Numerical Analysis*, 54(5):2951–2973, Jan. 2016.

[82] A. Pazy. *Semigroups of linear operators and applications to partial differential equations*, volume 44. Springer Science & Business Media, 2012.

[83] P. J. Phillips and M. F. Wheeler. A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity. *Computational Geosciences*, 12(4):417–435, Dec. 2008.

[84] K. Rajagopal and L. Tao. On the propagation of waves through porous solids. *International Journal of Non-Linear Mechanics*, 40(2-3):373–380, 2005.

[85] K. R. Rajagopal. On a hierarchy of approximate models for flows of incompressible fluids through porous solids. *Mathematical Models and Methods in Applied Sciences*, 17(02):215–252, Feb. 2007.

[86] E. Rohan, J. Turjanicová, and V. Lukeš. The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling. *Computers & Mathematics with Applications*, 78(9):3044–3066, 2019.

[87] R. Ruiz-Baier, M. Taffetani, H. D. Westermeyer, and I. Yotov. The Biot–Stokes coupling using total pressure: Formulation, analysis and application to interfacial flow in the eye. *Computer Methods in Applied Mechanics and Engineering*, page 30, 2022.

[88] T. F. Russell and M. F. Wheeler. Finite element and finite difference methods for continuous flows in porous media. In *The mathematics of reservoir simulation*, pages 35–106. SIAM, 1983.
[89] R. Sacco, P. Causin, C. Lelli, and M. T. Raimondi. A poroelastic mixture model of mechanobiological processes in biomass growth: Theory and application to tissue engineering. *Meccanica*, 52(14):3273-3297, Nov. 2017.

[90] R. Sacco, G. Guidoboni, and A. G. Mauri. *A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences*. Academic press, 2019.

[91] P. Saint-Macary. *Analyse Mathématique de Modèles de Diffusion En Milieu Poreux Élastique*. PhD thesis, Thesis Université de Pau et des Pays de l'Adour, 2004.

[92] J. E. Santos. Elastic wave propagation in fluid-saturated porous media. Part I. The existence and uniqueness theorems. *ESAIM: Mathematical Modelling and Numerical Analysis*, 20(1):113-128, 1986.

[93] M. Schanz. Poroelastodynamics: Linear Models, Analytical Solutions, and Numerical Methods. *Applied Mechanics Reviews*, 62(3):030803, May 2009.

[94] R. E. Showalter. Diffusion in poro-elastic media. *Journal of mathematical analysis and applications*, 251(1):310-340, 2000.

[95] R. E. Showalter. Poroelastic filtration coupled to Stokes flow. In *Control theory of partial differential equations*, pages 243-256. Chapman and Hall/CRC, 2005.

[96] R. E. Showalter. *Monotone operators in Banach space and nonlinear partial differential equations*, volume 49. American Mathematical Soc., 2013.

[97] R. E. Showalter and U. Stefanelli. Diffusion in poro-plastic media. *Mathematical Methods in the Applied Sciences*, 27(18):2131-2151, 2004.

[98] E. Storvik, J. W. Both, K. Kumar, J. M. Nordbotten, and F. A. Radu. On the optimization of the fixed-stress splitting for Biot's equations. *International Journal for Numerical Methods in Engineering*, 120(2):179-194, 2019.

[99] K. H. Støverud, M. Darcis, R. Helmig, and S. M. Hassanizadeh. Modeling concentration distribution and deformation during convection-enhanced drug delivery into brain tissue. *Transport in Porous Media*, 92(1):119-143, Oct. 2011.

[100] R. Temam. *Navier-Stokes equations: theory and numerical analysis*, volume 343. American Mathematical Soc., 2001.

[101] K. Terzaghi. *Theoretical soil mechanics*. Wiley, New York, 1943.

[102] K. Terzaghi, R. B. Peck, and G. Mesri. Soil mechanics. *New York: John Wiley & Sons*, 1996.

[103] B. Tully and Y. Ventikos. Cerebral water transport using multiple-network poroelastic theory: application to normal pressure hydrocephalus. *Journal of Fluid Mechanics*, 667:188-215, 2011.

[104] J. C. Vardakis, D. Chou, B. J. Tully, C. C. Hung, T. H. Lee, P.-H. Tsui, and Y. Ventikos. Investigating cerebral oedema using poroelasticity. *Medical Engineering & Physics*, 38(1):48-57, Jan. 2016.

[105] M. Verri, G. Guidoboni, L. Bociu, and R. Sacco. The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics. *Mathematical Biosciences and Engineering*, 15(4):933-959, 2018.

[106] M. Wheeler, G. Xue, and I. Yotov. Coupling multipoint flux mixed finite element methods with continuous Galerkin methods for poroelasticity. *Comput Geosci*, page 19, 2014.

[107] M. F. Wheeler and I. Yotov. A Multipoint Flux Mixed Finite Element Method. *SIAM Journal on Numerical Analysis*, 44(5):2082-2106, Jan. 2006.
[108] K. Wilmanski. Tortuosity and objective relative accelerations in the theory of porous materials. *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, 461(2057):1533-1561, May 2005.

[109] M. Yang and L. A. Taber. The possible role of poroelasticity in the apparent viscoelastic behavior of passive cardiac muscle. *Journal of biomechanics*, 24(7):587-597, 1991.

[110] S.-Y. Yi. A Study of Two Modes of Locking in Poroelasticity. *SIAM Journal on Numerical Analysis*, 55(4):1915-1936, Jan. 2017.

[111] A. Ženíšek. The existence and uniqueness theorem in Biot's consolidation theory. *Aplikace matematiky*, 29(3):194-211, 1984.

[112] O. C. Zienkiewicz and T. Shiomi. Dynamic behaviour of saturated porous media; The generalized Biot formulation and its numerical solution. *International Journal for Numerical and Analytical Methods in Geomechanics*, 8(1):71-96, 1984.