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

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2015
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Communications in Computational Physics. 2015, 17(5), pp. 1225-1245. ISSN 1815-2406. eISSN 1991-7120. Available under: doi: 10.4208/cicp.2014.m369
Zusammenfassung

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.

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Fachgebiet (DDC)
510 Mathematik
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Lattice Boltzmann method, convection-diffusion-reaction equation, L2 stability, L2 convergence
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ISO 690JUNK, Michael, Zhaoxia YANG, 2015. L2 Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations. In: Communications in Computational Physics. 2015, 17(5), pp. 1225-1245. ISSN 1815-2406. eISSN 1991-7120. Available under: doi: 10.4208/cicp.2014.m369
BibTex
@article{Junk2015Conve-32442,
  year={2015},
  doi={10.4208/cicp.2014.m369},
  title={L<sub>2</sub> Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations},
  number={5},
  volume={17},
  issn={1815-2406},
  journal={Communications in Computational Physics},
  pages={1225--1245},
  author={Junk, Michael and Yang, Zhaoxia}
}
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