# Convergence analysis for an exponentially fitted Finite Volume Method

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 6, page 1165-1188
- ISSN: 0764-583X

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topVanselow, Reiner. "Convergence analysis for an exponentially fitted Finite Volume Method." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1165-1188. <http://eudml.org/doc/197584>.

@article{Vanselow2010,

abstract = {
The paper is devoted to the convergence analysis of a well-known
cell-centered Finite Volume Method (FVM) for a
convection-diffusion problem in $\mathbb\{R\}^2$. 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.
},

author = {Vanselow, Reiner},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Convection-diffusion problem; cell-centered finite volume method;
Voronoi boxes; exponential fitting; convergence analysis;
nonconforming finite element method.; convergence; finite volume method; convection-diffusion problem; Voronoi box; Petrov-Galerkin finite element method},

language = {eng},

month = {3},

number = {6},

pages = {1165-1188},

publisher = {EDP Sciences},

title = {Convergence analysis for an exponentially fitted Finite Volume Method},

url = {http://eudml.org/doc/197584},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Vanselow, Reiner

TI - Convergence analysis for an exponentially fitted Finite Volume Method

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 6

SP - 1165

EP - 1188

AB -
The paper is devoted to the convergence analysis of a well-known
cell-centered Finite Volume Method (FVM) for a
convection-diffusion problem in $\mathbb{R}^2$. 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.

LA - eng

KW - Convection-diffusion problem; cell-centered finite volume method;
Voronoi boxes; exponential fitting; convergence analysis;
nonconforming finite element method.; convergence; finite volume method; convection-diffusion problem; Voronoi box; Petrov-Galerkin finite element method

UR - http://eudml.org/doc/197584

ER -

## References

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