| Issue |
ESAIM: M2AN
Volume 34, Number 6, November/December 2000
|
|
|---|---|---|
| Page(s) | 1165 - 1188 | |
| DOI | https://doi.org/10.1051/m2an:2000122 | |
| Published online | 15 April 2002 | |
Convergence analysis for an exponentially fitted Finite Volume Method
Dresden University of Technology, Department of Mathematics,
01062 Dresden, Germany. (vanselow@math.tu-dresden.de)
Received:
16
February
2000
Revised:
5
June
2000
Revised:
17
July
2000
The paper is devoted to the convergence analysis of a well-known
cell-centered Finite Volume Method (FVM) for a
convection-diffusion problem in 
. This FVM is based on Voronoi
boxes and
exponential fitting. To prove the convergence of the FVM, we use
a new nonconforming Petrov-Galerkin Finite Element Method (FEM)
for which the system of linear equations coincides completely with
that of the FVM. Thus, by proving convergence properties of the
FEM we obtain similar ones for the FVM. For the error estimation
of the FEM well-known statements have to be modified.
Mathematics Subject Classification: 65N12 / 65N99 / 65N30
Key words: Convection-diffusion problem / cell-centered finite volume method / Voronoi boxes / exponential fitting / convergence analysis / nonconforming finite element method.
© EDP Sciences, SMAI, 2000
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