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Volume 17, Issue 5
$L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations

Michael Junk & Zhaoxia Yang

DOI: 10.4208/cicp.2014.m369

Commun. Comput. Phys., 17 (2015), pp. 1225-1245.

Published online: 2018-04

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  • Abstract

Combining asymptotic analysis and weighted $L_2$ 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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@Article{CiCP-17-1225, author = {Michael Junk and Zhaoxia Yang}, title = {$L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {5}, pages = {1225--1245}, abstract = {

Combining asymptotic analysis and weighted $L_2$ 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2014.m369}, url = {http://global-sci.org/intro/article_detail/cicp/11010.html} }
TY - JOUR T1 - $L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations AU - Michael Junk & Zhaoxia Yang JO - Communications in Computational Physics VL - 5 SP - 1225 EP - 1245 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.2014.m369 UR - https://global-sci.org/intro/article_detail/cicp/11010.html KW - AB -

Combining asymptotic analysis and weighted $L_2$ 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.

Michael Junk and Zhaoxia Yang. (2018). $L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations. Communications in Computational Physics. 17 (5). 1225-1245. doi:10.4208/cicp.2014.m369
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