Numerical Reliability for Mixed Methods Applied to Flow Problems in Porous Media

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Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures (2008, methodology): “The resulting linear system is SPD whose primary unknowns are the face-potentials Kw on the grid edges, that is, ðM RTD 1RÞKw ¼ RTD 1F þ V ð27Þ The preconditioned conjugate gradient (PCG) solver with the Eisenstat diagonal preconditioner [85] is found to be efficient for Eq.”
Compositional Modeling by the Combined Discontinuous Galerkin and Mixed Methods (2004, background): “11, one may refer to Chavent and Roberts (1991) and Hoteit et al. (2002).”
A mixed hybrid Mortar method for solving flow in discrete fracture networks (2010, methodology): “Here we follow the methodology presented in 2 , 7 .”
Mixed finite elements for solving 2‐D diffusion‐type equations (2010, methodology): “[81] The MHFE method yields a symmetric and positive definite matrix which generally does not satisfy the M matrix property [Hoteit et al., 2002a, 2002b; Mazzia, 2008; Younes and Fontaine, 2008a].”
Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media (2005, methodology): “The velocity field is approximated in the so-called RaviartThomas space of lowest order (RT0) [see, e.g., Chavent and Roberts, 1991; Hoteit et al., 2002].”