$L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations

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.