Relationships among some locally conservative discretization methods which handle discontinuous coefficients |
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| Authors: | Email author" target="_blank">R?A?KlausenEmail author T?F?Russell |
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| Institution: | (1) Department of Informatics and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1080, Blindern, 0316 Oslo 3, Norway;(2) Department of Mathematics, University of Colorado at Denver, P.O. Box 173364, Campus Box 170, Denver, CO 80217-3364, USA |
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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.
T.F. Russell: Partially supported by the National Science Foundation Grant Nos. DMS-0084438 and DMS-0222300. |
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| 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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