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Combining an asymptotic analysis of the lattice Boltzmann method [M. Junk, Z. Yang, Asymptotic analysis of lattice Boltzmann boundary conditions, J. Stat. Phys. 121 (2005) 3–35] with the stability estimate presented in [M. Junk, W.-A. Yong, Weighted L2 stability of the lattice Boltzmann equation, Preprint], we are able to prove some strict convergence results. The proof applies to the lattice Boltzmann...
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