Diffusion in Poro-Elastic Media

By R. Showalter. 2000

345 citations recorded by the source corpus.

Existence, uniqueness, and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/873eef1058bde386bdb1ea4e058063faa470f867

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In Mechanics of Materials

Citations in the corpus

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity (2013, methodology): “The poroelasticity system [6, 42] in over a time interval (0, T ], T > 0, reads −∇·σ = f, in × (0, T ], (2.”
A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems (2009, background): “[17] R. E. Showalter.”
Stability and monotonicity for some discretizations of the Biot’s consolidation model (2015, neutral): “Results on the existence and uniqueness of the solution for these models have been investigated by Showalter in [4] and by Zenisek in [5], and the well-posedness for nonlinear poroelastic models is considered, for example, in [6].”
Finite element methods in linear poroelasticity: theoretical and computational results (2005, background): “As discussed in the Introduction, theoretical properties of solutions in linear poroelasticity have been developed in Zenisek [1984] for the case co = 0, and for the general case in Showalter [2000], who uses a semigroup approach.”
Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics (2016, background): “The existence, uniqueness, and regularity of the Biot system have been investigated by a number of authors (Showalter [23], Phillips & Wheeler [19], and Girault et al [12]).”
Analysis of a multiphysics finite element method for a poroelasticity model (2018, methodology): “We refer the reader to Terzaghi (1943), Coussy (2004) and Phillips & Wheeler (2007a) for a derivation of the model and to Schowalter (2000) for its mathematical analysis.”
A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity (2008, methodology): “The poroelasticity equations consist of a momentum and a mass conservation equation, and they are derived at the macroscopic scale in the work of Terzaghi [27] and Biot [4, 5]. In our discussion of the equations, we follow the presentation of Showalter [ 26 ].”
A coupling of nonconforming and mixed finite element methods for Biot's consolidation model (2013, background): “(4b) The existence, uniqueness, and regularity theory of the solution of the system (2) was studied by Showalter [34].”
A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case (2007, methodology): “The poroelasticity equations consist of a momentum and a mass conservation equation and are derived at the macroscopic scale in the work of Terzaghi [31 ]a nd Biot [2, 3]. In our discussion of the equations, we follow the presentation of Showalter [ 28 ].”
Convergence analysis of a new mixed finite element method for Biot's consolidation model (2014, background): “The existence, uniqueness, and regularity of the initial-boundary value problem (1)–(3)–(4) has been studied by Showalter [23, 24].”
Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium (2016, background): “Biot systems without fractures have been analyzed by a number of authors who established existence, uniqueness, and regularity, see Showalter [30] and references therein, Phillips and Wheeler [26], Girault et al. [15].”