# A Posteriori Error Estimates for Finite Volume Approximations

S. Cochez-Dhondt; S. Nicaise; S. Repin

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 1, page 106-122
- ISSN: 0973-5348

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topCochez-Dhondt, S., Nicaise, S., and Repin, S.. "A Posteriori Error Estimates for Finite Volume Approximations." Mathematical Modelling of Natural Phenomena 4.1 (2009): 106-122. <http://eudml.org/doc/222441>.

@article{Cochez2009,

abstract = {
We present new a posteriori error estimates for the finite volume approximations
of elliptic problems. They are obtained by applying functional a posteriori
error estimates to natural extensions of the approximate solution and its flux
computed by the finite volume method. The estimates give guaranteed upper bounds
for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and
also in terms of the combined primal-dual norms. It is shown that the estimates
provide sharp upper and lower bounds of the error and their practical
computation requires solving only finite-dimensional problems.},

author = {Cochez-Dhondt, S., Nicaise, S., Repin, S.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {finite volume methods; elliptic problems; a posteriori error estimates
of the functional type; a posteriori error estimates; numerical examples},

language = {eng},

month = {1},

number = {1},

pages = {106-122},

publisher = {EDP Sciences},

title = {A Posteriori Error Estimates for Finite Volume Approximations},

url = {http://eudml.org/doc/222441},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Cochez-Dhondt, S.

AU - Nicaise, S.

AU - Repin, S.

TI - A Posteriori Error Estimates for Finite Volume Approximations

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/1//

PB - EDP Sciences

VL - 4

IS - 1

SP - 106

EP - 122

AB -
We present new a posteriori error estimates for the finite volume approximations
of elliptic problems. They are obtained by applying functional a posteriori
error estimates to natural extensions of the approximate solution and its flux
computed by the finite volume method. The estimates give guaranteed upper bounds
for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and
also in terms of the combined primal-dual norms. It is shown that the estimates
provide sharp upper and lower bounds of the error and their practical
computation requires solving only finite-dimensional problems.

LA - eng

KW - finite volume methods; elliptic problems; a posteriori error estimates
of the functional type; a posteriori error estimates; numerical examples

UR - http://eudml.org/doc/222441

ER -

## References

top- A. Agouzal, F. Oudin. A posteriori error estimator for finite volume methods. C. R. Acad. Sci. Paris, Sér. 1, 343 (2006), 349–354. Zbl1023.65116
- S. Repin, S. Sauter, A. Smolianski. Two-Sided a posteriori error estimates for mixed formulations of elliptic problems. Preprint 21-2005, Institute of Mathematics, University of Zurich (to appear in SIAM J. Numer. Anal.). Zbl1185.35048
- R. Verfürth. A review of a posteriori error estimation and adaptive mesh–refinement techniques. Wiley, Teubner, New York, 1996. Zbl0853.65108
- M. Vohralík. A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. ESAIM: Proc., 18 (2007), 57–69. Zbl05213256

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