{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T01:48:36Z","timestamp":1773366516104,"version":"3.50.1"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,11,28]],"date-time":"2008-11-28T00:00:00Z","timestamp":1227830400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2009,3]]},"DOI":"10.1007\/s00211-008-0196-0","type":"journal-article","created":{"date-parts":[[2008,11,27]],"date-time":"2008-11-27T12:32:42Z","timestamp":1227789162000},"page":"65-87","source":"Crossref","is-referenced-by-count":40,"title":["Convergence of lattice Boltzmann methods for Navier\u2013Stokes flows in periodic and bounded domains"],"prefix":"10.1007","volume":"112","author":[{"given":"Michael","family":"Junk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaoxia","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,11,28]]},"reference":[{"key":"196_CR1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10955-005-7010-5","volume":"121","author":"A. Caiazzo","year":"2005","unstructured":"Caiazzo A.: Analysis of lattice Boltzmann initialization routines. J. Stat. Phys. 121, 37\u201348 (2005)","journal-title":"J. Stat. Phys."},{"key":"196_CR2","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1137\/0917052","volume":"17","author":"B. Elton","year":"1996","unstructured":"Elton B.: Comparison of lattice Boltzmann and finite difference methods for a two-dimensional viscous Burgers equation. SIAM J. Sci. Comp. 17, 783\u2013813 (1996)","journal-title":"SIAM J. Sci. Comp."},{"key":"196_CR3","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1137\/0732062","volume":"32","author":"B. Elton","year":"1995","unstructured":"Elton B., Levermore C., Rodrigue G.: Convergence of convective diffusive lattice Boltzmann methods. SIAM J. Numer. Anal. 32, 1327\u20131354 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"196_CR4","first-page":"649","volume":"1","author":"U. Frisch","year":"1987","unstructured":"Frisch U., d\u2019Humi\u00e8res D., Hasslacher B., Lallemand P., Pomeau Y., Rivet J.P.: Lattice gas hydrodynamics in two and three dimensions. Complex Syst. 1, 649\u2013707 (1987)","journal-title":"Complex Syst."},{"key":"196_CR5","doi-asserted-by":"crossref","first-page":"6333","DOI":"10.1103\/PhysRevE.55.R6333","volume":"55","author":"X. He","year":"1997","unstructured":"He X., Luo L.-S.: A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55, 6333\u20136336 (1997)","journal-title":"Phys. Rev. E"},{"key":"196_CR6","doi-asserted-by":"crossref","first-page":"6811","DOI":"10.1103\/PhysRevE.56.6811","volume":"56","author":"X. He","year":"1997","unstructured":"He X., Luo L.-S.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811\u20136817 (1997)","journal-title":"Phys. Rev. E"},{"key":"196_CR7","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.jcp.2005.05.003","volume":"210","author":"M. Junk","year":"2005","unstructured":"Junk M., Klar A., Luo L.-S.: Asymptotic analysis of the lattice Boltzmann equation. J. Comp. Phys. 210, 676\u2013704 (2005)","journal-title":"J. Comp. Phys."},{"key":"196_CR8","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.1016\/j.camwa.2007.08.002","volume":"55","author":"M. Junk","year":"2008","unstructured":"Junk M., Yang Z.: Convergence of lattice Boltzmann methods for Stokes flows in periodic and bounded domains. Comp. Math. Appl. 55, 1481\u20131491 (2008)","journal-title":"Comp. Math. Appl."},{"key":"196_CR9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10955-005-8321-2","volume":"121","author":"M. Junk","year":"2005","unstructured":"Junk M., Yang Z.: Asymptotic analysis of lattice Boltzmann boundary conditions. J. Stat. Phys. 121, 3\u201335 (2005)","journal-title":"J. Stat. Phys."},{"key":"196_CR10","doi-asserted-by":"crossref","unstructured":"Junk, M., Yong, W.A.: Weighted L 2 stability of the lattice Boltzmann method. SIAM J. Numer. Anal. (in press)","DOI":"10.1137\/060675216"},{"key":"196_CR11","first-page":"165","volume":"35","author":"M. Junk","year":"2003","unstructured":"Junk M., Yong W.A.: Rigorous Navier\u2013Stokes limit of the lattice Boltzmann equation. Asymptot. Anal. 35, 165\u2013184 (2003)","journal-title":"Asymptot. Anal."},{"key":"196_CR12","doi-asserted-by":"crossref","first-page":"6546","DOI":"10.1103\/PhysRevE.61.6546","volume":"61","author":"P. Lallemand","year":"2000","unstructured":"Lallemand P., Luo L.-S.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability. Phys. Rev. E 61, 6546\u20136562 (2000)","journal-title":"Phys. Rev. E"},{"key":"196_CR13","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1016\/j.compfluid.2005.08.008","volume":"35","author":"R. Mei","year":"2006","unstructured":"Mei R., Luo L.-S., Lallemand P., d\u2019Humieres D.: Consistent initial conditions for lattice Boltzmann simulations. Comput. Fluids 35, 855\u2013862 (2006)","journal-title":"Comput. Fluids"},{"key":"196_CR14","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1006\/jcph.1999.6334","volume":"155","author":"R. Mei","year":"1999","unstructured":"Mei R., Luo L.-S., Shyy W.: An accurate curved boundary treatment in the lattice Boltzmann method. J. Comp. Phys. 155, 307\u2013330 (1999)","journal-title":"J. Comp. Phys."},{"key":"196_CR15","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1006\/jcph.1996.0016","volume":"123","author":"J.D. Sterling","year":"1996","unstructured":"Sterling J.D., Chen S.: Stability analysis of lattice Boltzmann methods. J. Comp. Phys. 123, 196\u2013206 (1996)","journal-title":"J. Comp. Phys."},{"key":"196_CR16","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF01386051","volume":"6","author":"G. Strang","year":"1964","unstructured":"Strang G.: Accurate partial difference methods ii. non-linear problems. Numer. Math. 6, 37\u201364 (1964)","journal-title":"Numer. Math."},{"key":"196_CR17","doi-asserted-by":"crossref","first-page":"2243","DOI":"10.1103\/PhysRevE.56.2243","volume":"56-2","author":"R.A. Worthing","year":"1997","unstructured":"Worthing R.A., Mozer J., Seeley G.: Stability analysis of lattice Boltzmann methods. Phys. Rev. E 56-2, 2243\u20132253 (1997)","journal-title":"Phys. Rev. E"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-008-0196-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-008-0196-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-008-0196-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:41Z","timestamp":1558628561000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-008-0196-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,11,28]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["196"],"URL":"https:\/\/doi.org\/10.1007\/s00211-008-0196-0","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,11,28]]}}}