Compact Multiscale Finite Volume Method for Heterogeneous Anisotropic Elliptic Equations

2008 ◽  
Vol 7 (2) ◽  
pp. 934-962 ◽  
Author(s):  
Marc A. Hesse ◽  
Bradley T. Mallison ◽  
Hamdi A. Tchelepi
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Multiscale Finite Volume ◽  
Volume Method ◽  
Anisotropic Elliptic Equations

Analysis of a New Mixed Finite Volume Method

2003 ◽  
Vol 3 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Ilya D. Mishev
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Variable Pressure ◽  
Order Error ◽  
First Order ◽  
Scalar Variable ◽  
Volume Method ◽  
Well Posed ◽  
Theoretical Results

AbstractA new mixed finite volume method for elliptic equations with tensor coefficients on rectangular meshes (2 and 3-D) is presented. The implementation of the discretization as a finite volume method for the scalar variable (“pressure”) is derived. The scheme is well suited for heterogeneous and anisotropic media because of the generalized harmonic averaging. It is shown that the method is stable and well posed. First-order error estimates are derived. The theoretical results are confirmed by the presented numerical experiments.

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