References
- Mandel J. Consolidation des sols (étude mathématique). Géotechnique. 1953;3(7):287–299.
- Coussy O. Poromechanics. Chichester: John Wiley and Sons; 2004.
- Verruijt A. Theory and problems of poroelasticity. Delft: Delft University of Technology; 2014.
- Abousleiman Y, Cheng AD, Cui L, et al. Mandel's problem revisited. Géotechnique. 1996;46(2):187–195.
- Phillips PJ, Wheeler MF. A coupling of mixed and continuous Galerkin finite elements methods for poroelasticity I: the continous in time case. Comput Geosci. 2007;11:131–144.
- Gai X. A coupled geomechanics and reservoir flow model on parallel computers [PhD thesis]. The University of Texas at Austin; 2004.
- Guzman H. Domain decomposition methods in geomechanics [PhD thesis]. The University of Texas at Austin; 2012.
- Liu R. Discontinuous Galerkin finite element solution for poromechanics [PhD thesis]. The University of Texas at Austin; 2004.
- Wick T. Numerical methods for partial differential equations. Institutionelles Repositorium der Leibniz Universität Hannover, 2022. p. 442. doi:10.15488/11709.
- Gibson RE, Knights K, Taylor PW. A critical experiment to examine theories of thrree-dimensional consolidation. Proc Enr Conf Soil Mech Wiesbaden. 1963;1:69–76.
- Verruijt A. Discussion on consolidation of a massive sphere. In: Proc. 6th Int. Conf. Soil Mech. Montreal. Vol. 3. 1965. p. 401–402.
- Cao Y, Chen S, Meir AJ. Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete Contin Dyn Syst Ser B. 2013;18:1253–1273.
- van Duijn CJ, Mikelić A. Mathematical theory of nonlinear single-phase poroelasticity. preprint of the Darcy Center Eindhoven-Utrecht, The Netherlands, June 2019. Available from: www.darcycenter.org/wp-content/uploads/2019/06/Duijn-and-Mikelic-2019-5.pdf.
- Bociu L, Guidoboni G, Sacco R, et al. Analysis of nonlinear poro-elastic and poro-visco-elastic models. Arch Ration Mech Anal. 2016;222:1445–1519.
- Bociu B, Webster JT. Nonlinear quasi-static poroelasticity. J Differ Equ. 2021;296:242–278.
- Bociu L, Muha B, Webster JT. Weak solutions in nonlinear poroelasticity with incompressible constituents. arXiv: 2108.10977. 2022.
- van Duijn CJ, Mikelić A, Wick T. A monolithic phase-field model of a fluid-driven fracture in a nonlinear poroelastic medium. Math Mech Solids. 2019;24:1530–1555.
- Bosco E, Peerlings RH, Geers MG. Predicting hygro-elastic properties of paper sheets based on an idealized model of the underlying fibrous network. Int J Solids Struct. 2015;56:43–52.
- Canic S, Hartley CJ, Rosenstrauch D, et al. Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics and experimental validation. Ann Biomed Eng. 2006;34:575–592.
- Prosi M, Zunino P, Perktold K, et al. Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: a new methodology for the model set up with applications to the study of disturbed lumenal flow. J Biomech. 2005;38:903–917.
- Bedford A, Drumheller DS. A variational theory of immiscible mixtures. Arch Ration Mech Anal. 1978;68(1):37–51.
- Bedford A, Drumheller DS. Theories of immiscible and structured mixtures. Int J Engin Sci. 1983;21(8):863–960.
- Rutqvist J, Börgesson L, Chijimatsu M, et al. Thermohydromechanics of partially saturated geological media: governing equations and formulation of four finite element models. Int J Rock Mech Min Sci. 2001;38:105–127.
- Lewis RW, Schrefler BA. The finite element method in the static and dynamic deformation and consolidation of porous media. Chichester: John Wiley and Sons; 1998.
- Bear J, Bachmat Y. Introduction to modeling of transport phenomena in porous media. Dordrecht, The Netherlands: Kluwer Academic Publishers; 1990.
- Biot MA. Mechanics of deformation and acoustic propagation in porous media. J Appl Phys. 1962;33:1482.
- Murad MA, Cushman JH. Multiscale flow and deformation in hydrophilic swelling porous media. Int J Engin Sci. 1996;34:313–338.
- Roubiček T. Nonlinear partial differential equations with applications. Edition 2, Basel: Birkhäuser; 2013.
- Cryer CW. A comparison of the three dimensional consolidation threories of Biot and Terzaghi. Q J Mech Appl Math. 1963;16:401–412.
- van Duijn CJ, Mikelić A. Mathematical proof of the Mandel–Cryer effect in poroelasticity. Multiscale Model Simul. 2021;19(1):550-–567.
- Lions JL. Quelques méthodes de résolution des problémes aux limites non linéaires. Paris: Dunod; 1969.
- Zeidler E. Nonlinear functional analysis and its applications II/B nonlinear monotone operators. New York: Springer-Verlag; 1990.
- Mikelić A, Wang B, Wheeler MF. Numerical convergence study of iterative coupling for coupled flow and geomechanics. Comput Geosci. 2014;18:325–341.
- Ciarlet PG. The finite element method for elliptic problems. Edition 1, Vol. 4, North-Holland; 1978.
- Wick T. Multiphysics phase-field fracture: modeling, adaptive discretizations, and solvers. de Gruyter; 2020. (Radon Series on Computational and Applied Mathematics, Band 28).
- Goll C, Wick and W. Wollner T. DOpElib: differential equations and optimization environment; a goal oriented software library for solving PDEs and optimization problems with PDEs. Archive Numer Softw. 2017;5(2):1–14.
- Arndt D, Bangerth W, Clevenger TC, et al. The deal.II library, version 9.1. J Numer Math. 2019;27(4):203–213.
- The differential equation and optimization environment: DOpElib. http://www.dopelib.net, last accessed Oct 23, 2021.
- Girault V, Pencheva G, Wheeler MF, et al. Domain decomposition for poroelasticity and elasticity with DG jumps and mortars. Math Models Methods Appl Sci. 2011;21:169-–213.
- Boyer F, Fabrie P. Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. Springer Science & Business Media; 2012. (Applied Mathematical Sciences Vol. 183).
- Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York, NY: Springer Science and Business Media, Springer; 2011.