@Article{CiCP-17-1225, author = {}, 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} }