A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

By P. Phillips, Mary F. Wheeler. 2007

290 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/57781206c5a3b335646276126babd587d0adf10d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanical Engineering

Citations in the corpus

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 [28] and references therein, Phillips &Wheeler [26], Girault et al [15].”
Finite element methods in linear poroelasticity: theoretical and computational results (2005, background): “It suffices here to mention that Phillips and Wheeler [2005b] first proposed a scheme based on discontinuous Galerkin elements for the deformation and a mixed space for flow.”
A coupling of nonconforming and mixed finite element methods for Biot's consolidation model (2013, methodology): “The following lemma regarding time derivatives will play an important role to develop error estimates [18].”
Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity (2013, methodology): “A formulation based on mixed finite element (MFE) methods for flow and continuous Galerkin (CG) for elasticity has been proposed in [36, 37].”
Convergence analysis of a new mixed finite element method for Biot's consolidation model (2014, methodology): “For a comparison purpose, we solved the problem using a coupled CG/mixed method [3, 4] that uses continuous bilinear elements for the displacement and the lowest-order Raviart–Thomas space for the flow variables and also using our new mixed finite element method.”
Sequential methods for coupled geomechanics and multiphase flow (2010, methodology): “A converged solution is obtained through iteration, typically using the Newton–Raphson method (Lewis and Sukirman, 1993; Wan et al., 2003; Jha and Juanes, 2007; Jean et al., 2007; Phillips and Wheeler, 2007a,b; Pan et al., 2009).”
A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity (2008, background): “The algorithmic development and results herein represent the natural extension of our work in Phillips and Wheeler [ 17 ], where the displacements were approximated by continuous Galerkin elements.”
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]).”
On the optimization of the fixed‐stress splitting for Biot's equations (2018, background): “Subtract (5) and (6) from (3) and (4), respectively, to obtain the error equations ⎪⎨⎪⎩ (i) 2μ ⟨”
Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach (2009, methodology): “We now turn to Barry and Mercer’s problem [2], which involves only the case that co = 0. The problem involves a point-source (at (0.25, 0.25)) on the unit domain with boundary conditions contrived in order to admit an analytical solution. In [ 13 ], we measure the”