$L_2$ Convergence of the Lattice Boltzmann Method for One Dimensional Convection-Diffusion-Reaction Equations (Communications in Computational Physics, 2018)
Combining asymptotic analysis and weighted $L_2$ stability estimates, theconvergence of lattice Boltzmann methods for the approximation of 1D convection-diffusion-reactionequations is proved. Unlike previous approaches, the proof doesnot require transformations to equivalent macroscopic equations.