Computational Geosciences

, Volume 8, Issue 4, pp 341–377 | Cite as

Relationships among some locally conservative discretization methods which handle discontinuous coefficients

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Abstract

This paper presents the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation. The methods discussed are the classical mixed finite element method (MFEM), the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control-volume method. These methods are all locally mass conservative, and handle general irregular grids with anisotropic and heterogeneous discontinuous permeability. In addition to this, the methods have a common weak continuity in the pressure across the edges, which in some cases corresponds to Lagrange multipliers. It seems that this last property is an essential common quality for these methods.

Keywords

relationships mixed finite element method (MFEM) expanded mixed finite element method (EMFEM) enhanced cell-centered finite difference method (ECCFDM) control-volume mixed finite element method (CVMFEM) support operator method (SOM) multi-point flux-approximation (MPFA) control-volume method 
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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Informatics and Centre of Mathematics for ApplicationsUniversity of OsloOslo 3Norway
  2. 2.Department of MathematicsUniversity of Colorado at DenverDenverUSA

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