L2Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations | Zendy

Michael Junk | Zendy; Zhaoxia Yang | Zendy

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L₂Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations

Author(s) -

Michael Junk,

Zhaoxia Yang

Publication year - 2015

Publication title -

communications in computational physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.217

H-Index - 56

eISSN - 1991-7120

pISSN - 1815-2406

DOI - 10.4208/cicp.2014.m369

Subject(s) - lattice boltzmann methods , convergence (economics) , convection , convection–diffusion equation , mathematics , boltzmann equation , diffusion , reaction–diffusion system , hpp model , boltzmann constant , physics , lattice (music) , stability (learning theory) , mathematical analysis , statistical physics , mechanics , thermodynamics , computer science , reynolds number , acoustics , turbulence , economics , economic growth , machine learning

Combining asymptotic analysis andweighted L2 stability estimates, the convergence of lattice Boltzmannmethods for the approximation of 1D convection-diffusionreaction equations is proved. Unlike previous approaches, the proof does not require transformations to equivalent macroscopic equations.

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