Control‐volume mixed finite element methods
 Z. Cai,
 J.E. Jones,
 S.F. McCormick,
 T.F. Russell
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A key ingredient in simulation of flow in porous media is accurate determination of the velocities that drive the flow. Large‐scale irregularities of the geology (faults, fractures, and layers) suggest the use of irregular grids in simulation. This paper presents a control‐volume mixed finite element method that provides a simple, systematic, easily implemented procedure for obtaining accurate velocity approximations on irregular (i.e., distorted logically rectangular) block‐centered quadrilateral grids. The control‐volume formulation of Darcy’s law can be viewed as a discretization into element‐sized “tanks” with imposed pressures at the ends, giving a local discrete Darcy law analogous to the block‐by‐block conservation in the usual mixed discretization of the mass‐conservation equation. Numerical results in two dimensions show second‐order convergence in the velocity, even with discontinuous anisotropic permeability on an irregular grid. The method extends readily to three dimensions.
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 Title
 Control‐volume mixed finite element methods
 Journal

Computational Geosciences
Volume 1, Issue 34 , pp 289315
 Cover Date
 19970901
 DOI
 10.1023/A:1011577530905
 Print ISSN
 14200597
 Online ISSN
 15731499
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 control‐volume method
 mixed method
 local mass conservation
 local Darcy law
 block‐centered grid
 distorted grid
 anisotropy
 heterogeneity
 Industry Sectors
 Authors

 Z. Cai ^{(1)}
 J.E. Jones ^{(2)}
 S.F. McCormick ^{(3)}
 T.F. Russell ^{(4)}
 Author Affiliations

 1. Center for Applied Mathematics, Purdue University, West Lafayette, IN, 47907‐1395, USA
 2. Lawrence Livermore National Laboratory, MS L‐316, P.O. Box 808, Livermore, CA, 94551‐0808, USA
 3. Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO, 80309‐0526, USA
 4. Department of Mathematics, University of Colorado at Denver, Campus Box 170, Denver, CO, 80217‐3364, USA