scholarly journals Validation of a 2D cell-centered Finite Volume method for elliptic equations

2019 ◽  
Vol 165 ◽  
pp. 119-138 ◽  
Author(s):  
Gung-Min Gie ◽  
Chang-Yeol Jung ◽  
Thien Binh Nguyen
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Volume Method

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.

Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

2015 ◽  
Vol 7 (4) ◽  
pp. 454-471
Author(s):  
Yanli Chen ◽  
Yonghai Li
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Stiffness Matrix ◽  
Finite Volume Methods ◽  
Matrix Analysis ◽  
Quadrilateral Meshes ◽  
Analysis Technique ◽  
The Stability ◽  
Volume Method

AbstractIn this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal convergence rate in H1 norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

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