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L<sub>2</sub> Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations

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

Type of Publication: Journal article
Publication status: Published
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-0-296731
Author: Junk, Michael; Yang, Zhaoxia
Year of publication: 2015
Published in: Communications in Computational Physics ; 17 (2015), 5. - pp. 1225-1245. - ISSN 1815-2406. - eISSN 1991-7120
DOI (citable link): https://dx.doi.org/10.4208/cicp.2014.m369
Summary:
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.
Subject (DDC): 510 Mathematics
Keywords: Lattice Boltzmann method, convection-diffusion-reaction equation, L2 stability, L2 convergence
Link to License: Terms of use
Bibliography of Konstanz: Yes
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JUNK, Michael, Zhaoxia YANG, 2015. L2 Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations. In: Communications in Computational Physics. 17(5), pp. 1225-1245. ISSN 1815-2406. eISSN 1991-7120. Available under: doi: 10.4208/cicp.2014.m369

@article{Junk2015Conve-32442, title={L2 Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations}, year={2015}, doi={10.4208/cicp.2014.m369}, number={5}, volume={17}, issn={1815-2406}, journal={Communications in Computational Physics}, pages={1225--1245}, author={Junk, Michael and Yang, Zhaoxia} }

2015 L<sub>2</sub> Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations terms-of-use 2015-12-16T10:04:22Z Yang, Zhaoxia Junk, Michael eng Junk, Michael Yang, Zhaoxia 2015-12-16T10:04:22Z Combining asymptotic analysis and weighted L<sub>2</sub> 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.

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