Multidomain mixed variational analysis of transport flow through elastoviscoplastic porous media

References

• Alduncin G . Composition duality methods for evolution mixed variational inclusions. Nonlinear Anal Hybrid Syst. 2007;1:336–363.
   Web of Science ®Google Scholar
• Alduncin G . Composition duality principles for evolution mixed variational inclusions. Appl Math Lett. 2007;20:734–740.
   Web of Science ®Google Scholar
• Alduncin G . Primal and dual evolution macro-hybrid mixed variational inclusions. Int J Math Anal. 2011;5:1631–1664.
   Google Scholar
• Alduncin G . Composition duality methods for mixed variational inclusions. Appl Math Optim. 2005;52:311–348.
   Web of Science ®Google Scholar
• Showalter RE , Stefanelli U . Diffusion in poro-plastic media. Math Meth Appl Sci. 2004;27:2131–2151.
   Web of Science ®Google Scholar
• Phillips PJ , Wheeler MF . A coupling of mixed and discontinuous Galerkin fnite-element methods for poroelasticity. Comput Geosci. 2008;12:417–435.
   Web of Science ®Google Scholar
• Girault V , Pencheva G , Wheeler MF , et al . Domain decomposition for poroelasticity and elasticity with DG jumps and mortars. Math Models Meth Appl Sci. 2011;21:169–213.
   Web of Science ®Google Scholar
• Mikelić A , Wheeler MF . On the interface law between a deformable porous medium containing a viscous fluid and an elastic body. Math Models Methods Appl Sci. 2012;22:1250031.
   Web of Science ®Google Scholar
• Rohan E , Shaw S , Wheeler MF , et al . Mixed and Galerkin finite element approximation of flow in a linear viscoelastic porous medium. Comput Methods Appl Mech Eng. 2013;260:78–91.
   Web of Science ®Google Scholar
• Girault V , Kumar K , Wheeler MF . Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Comput Geosci. 2016;20:997–1011.
   Web of Science ®Google Scholar
• Alduncin G . Macro-hybrid mixed variational two-phase flow through fractured porous media. Math Meth Appl Sci. 2016;39:5242–5257.
   Web of Science ®Google Scholar
• Girault V , Raviart P-A . Finite element methods for Navier-Stokes equations. Berlin: Springer; 1986.
   Google Scholar
• Yosida K . Functional analysis. New York (NY): Springer-Verlag; 1974.
   Google Scholar
• Lions J-L . Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires [Some Resolution Methods for Nonlinear Differential Problems]. Paris: Dunod/Gauthier-Villars; 1969.
   Google Scholar
• Alduncin G . Composition duality principles for mixed variational inequalities. Math Comput Model. 2005;41:639–654.
   Google Scholar
• Alduncin G . Variational formulations of nonlinear constrained boundary value problems. Nonlinear Anal. 2010;72:2639–2644.
   Web of Science ®Google Scholar
• Duvaut G , Lions J-L . Les Inéquations en Méchanique et en Physique [Variational Inequalities in Mechanics and Physics]. Paris: Dunod; 1972.
   Google Scholar
• Ekeland I , Temam R . Analyse Convexe et Problèmes Variationnels [Convex Analysis and Variational Problems]. Paris: Dunod / Gauthier-Villars; 1974.
   Google Scholar
• de Marsil G . Quantitative hydrogeology for engineers. Cambridge (MA): Academic Press; 1986.
   Google Scholar
• Gurtin M , Fried E , Anand L . The mechanics and thermodynamics of continuum. Cambridge: Cambridge University Press; 2010.
   Google Scholar
• Alduncin G . Subdifferential and variational formulations of boundary value problems. Comput Methods Appl Mech Eng. 1989;72:173–186.
   Web of Science ®Google Scholar
• Quarteroni A , Valli A . Numerical approximation of partial differential equations. Berlin: Springer-Verlag; 1994.
   Google Scholar
• Showalter RE . Monotone operators in banach space and nonlinear partial differential equations. Providence: American Mathematical society; 1997.
   Google Scholar
• Chavent G , Jaffré J . Mathematical models and finite element for reservoir simulation. Amsterdam: North-Holland; 1986.
   Google Scholar
• Nair RS . The poromechanics of naturally fractured rock formations: a finite element approach PhD dissertation. Norman (OK): The University of Oklahoma; 2003.
   Google Scholar
• Halphen B , NGuyen QS . Sur les matériaux standard généralisés [On the Generalized Standard Materials]. J Mécanique. 1975;14:39–63.
   Web of Science ®Google Scholar
• Le Tallec P . Numerical analysis of viscoelastic problems. Paris: Masson; 1990.
   Google Scholar
• Perzyna P . Fundamental problems in viscoplasticity. Rec Adv Appl Mech. 1966;9:243–377.
   Google Scholar
• Prager W , Hodge P . The theory of perfectly plastic solids. New York (NY): Wiley; 1951.
   Google Scholar
• Alduncin G . Composition duality methods for quasistatic evolution elastoviscoplastic variational problems. Nonlinear Anal Hybrid Syst. 2011;5:113–122.
   Web of Science ®Google Scholar
• Temam R . A generalized Norton-Hoff model and the Prandt-Reuss law of plasticity. Arch Ration Mech Anal. 1986;95:137–183.
   Web of Science ®Google Scholar
• Rochdi M , Sofonea M . On frictionless contact between two elastic-viscoplastic bodies. Quart J Mech Appl Math. 1997;50:481–496.
   Web of Science ®Google Scholar
• Sofonea M , Renon N , Shillor M . Stress formulation for frictionless contact of an elastic-perfectly-plastic body. Appl Anal. 2004;83:1157–1170.
   Google Scholar
• Temam R . Analyse Numérique [Numerical Analysis]. Paris: Presses Universitaires de France; 1970.
   Google Scholar
• Fortin M , Glowinski R , editors. Méthodes de Lagrangien Augmenté: Applications à la Résolution Numérique de Problèmes aux Limites [Augmented Lagrangian Methods and Applications to the Numerical Resolution of Differential Problems]. Paris: Dunod-Bordas; 1982.
   Google Scholar
• Glowinski R , Le Tallec P . Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. Philadelphia (PA): SIAM; 1989.
   Google Scholar
• Dawson C , Sun S , Wheeler MF . Compatible algorithms for coupled flow and transport. Comput Methods Appl Mech Eng. 2004;193:2565–2580.
   Web of Science ®Google Scholar
• Dean RH , Stone CM , Minkoff SE . A comparison of techniques for coupling porous flow and geomechanics. SPE J. 2006;11:132–140.
   Web of Science ®Google Scholar
• Kim J , Tchelepi H , Juanes R . Stability and convergence of sequentiel methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput Methods Appl Mech Eng. 2011;200:1591–1606.
   Web of Science ®Google Scholar
• Kim J , Tchelepi HA , Juanes R . Accuracy and efficiency of sequential methods for coupled flow and geomechanics. SPE J. 2011;16:249–262.
   Web of Science ®Google Scholar
• Mikelić A , Wheeler MF . Convergence of iterative coupling for coupled flow and geomechanics. Comput Geosci. 2013;17:455–461.
   Web of Science ®Google Scholar
• Mikelić A , Wang B , Wheeler MF . Numerical convergence study of iterative coupling for coupled flow and geomechanics. Comput Geosci. 2014;18(3–4):325–341.
   Web of Science ®Google Scholar
• Castelletto N , White JA , Tchelepi HA . Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics. Numer Anal Methods Geomech. 2015;39:1593–1618.
   Web of Science ®Google Scholar