# Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron; Jacques Rappaz

- Volume: 47, Issue: 6, page 1765-1781
- ISSN: 0764-583X

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topFlotron, Stéphane, and Rappaz, Jacques. "Conservation schemes for convection-diffusion equations with Robin boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1765-1781. <http://eudml.org/doc/273326>.

@article{Flotron2013,

abstract = {In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some numerical examples which show the efficiency of the method.},

author = {Flotron, Stéphane, Rappaz, Jacques},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {finite elements; numerical conservation schemes; Robin boundary condition; convection-diffusion equations; Robin boundary conditions; finite element method; error bounds; stability; numerical experiment},

language = {eng},

number = {6},

pages = {1765-1781},

publisher = {EDP-Sciences},

title = {Conservation schemes for convection-diffusion equations with Robin boundary conditions},

url = {http://eudml.org/doc/273326},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Flotron, Stéphane

AU - Rappaz, Jacques

TI - Conservation schemes for convection-diffusion equations with Robin boundary conditions

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 6

SP - 1765

EP - 1781

AB - In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and we give some numerical examples which show the efficiency of the method.

LA - eng

KW - finite elements; numerical conservation schemes; Robin boundary condition; convection-diffusion equations; Robin boundary conditions; finite element method; error bounds; stability; numerical experiment

UR - http://eudml.org/doc/273326

ER -

## References

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- [7] A. Ern and J.-L. Guermond, Elements finis: Théorie, applications, mise en oeuvre. Springer-Verlag (2002). Zbl0993.65123MR1933883
- [8] S. Flotron, Simulations numériques de phénomènes MHD-thermique avec interface libre dans l’électrolyse de l’aluminium, Ph.D. Thesis, EPFL, Switzerland, expected in (2013).
- [9] T. Hofer, Numerical Simulation and optimization of the alumina distribution in an aluminium electrolysis pot, Ph.D. Thesis, Thesis No. 5023, EPFL, Switzerland (2011).
- [10] A. Quarteroni and A. Valli, Numerical approximation of partial differential equations. Springer Series in Computational Mathematics (1997). Zbl0803.65088MR1299729
- [11] R. Temam, Navier-Stokes equations. North-Holland (1984). Zbl0568.35002MR603444
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