Convergence analysis for an exponentially fitted Finite Volume Method

Reiner Vanselow

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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The paper is devoted to the convergence analysis of a well-known cell-centered Finite Volume Method (FVM) for a convection-diffusion problem in 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.

How to cite

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Vanselow, 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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