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L2 Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations

Published online by Cambridge University Press:  03 June 2015

Michael Junk  and
Zhaoxia Yang
Michael Junk
Affiliation:
FB Mathematik und Statistik, Universität Konstanz, Postfach D194, 78457 Konstanz, Germany
Zhaoxia Yang*
Affiliation:
FB Mathematik und Statistik, Universität Konstanz, Postfach D194, 78457 Konstanz, Germany
*
*Corresponding author. Email addresses: michael.junk@uni-konstanz.de (M. Junk), zhaoxia.yang@uni-konstanz.de (Z. Yang)
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Abstract

Combining asymptotic analysis and weighted L2 stability estimates, the convergence of lattice Boltzmann methods for the approximation of 1D convection-diffusion-reaction equations is proved. Unlike previous approaches, the proof does not require transformations to equivalent macroscopic equations.

Keywords

65417635Lattice Boltzmann methodconvection-diffusion-reaction equationL2 stabilityL2 convergence

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Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 5 , May 2015 , pp. 1225 - 1245
Copyright
Copyright © Global-Science Press 2015 

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