{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:10:52Z","timestamp":1787382652632,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains.<\/jats:p>\n                  <jats:p>This paper considers four Schwarz alternating methods for the N-dimensional, steady, viscous, incompressible Navier--Stokes equations, $N \\leq 4$. It is shown that the Schwarz sequences converge to the true solution provided that the Reynolds number is sufficiently small.<\/jats:p>","DOI":"10.1137\/s1064827598347411","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1974-1986","source":"Crossref","is-referenced-by-count":15,"title":["On Schwarz Alternating Methods for the Incompressible Navier--Stokes Equations"],"prefix":"10.1137","volume":"22","author":[{"given":"S. H.","family":"Lui","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1090464-8"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596304046"},{"key":"R3","unstructured":"E. Dean, Q. Dinh, R. Glowinski, Jiwen He, T.\u2010W. Pan, J. P\u00e9riaux, Least squares\/domain imbedding methods for Neumann problems: applications to fluid dynamics, SIAM, Philadelphia, PA, 1992, 451\u201347593h:65152"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02510214"},{"key":"R5","unstructured":"M. Dryja and O. B. Widlund,\n                      An Additive Variant of the Schwarz Alternating Method for the Case of Many Subregions\n                      , Technical report 339, Courant Institute, New York University, New York, 1987."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/PL00000950"},{"key":"R7","unstructured":", First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Proceedings of the symposium held in Paris, January 7\u20139, 1987, Society for Industrial and Applied Mathematics (SIAM), 1988, 0\u20130, x+43189f:65005"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"D. K. Kaushik, D. E. Keyes, and B. F. Smith,\n                      On the interaction of architecture and algorithm in the domain\u2010based parallelization of an unstructured\u2010grid incompressible flow code\n                      , in Domain Decomposition Methods 10, J. Mandel, C. Farhat, and X.\u2010C. Cai, eds., AMS, Providence, RI, 1998, pp. 287\u2013295.","DOI":"10.1090\/conm\/218\/3020"},{"key":"R9","unstructured":"P.\u2010L. Lions, On the Schwarz alternating method. I, SIAM, Philadelphia, PA, 1988, 1\u20134290a:65248"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597327553"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996297461"},{"key":"R12","unstructured":"R. Temam,\n                      Navier\u2013Stokes Equations\n                      , North Holland, Amsterdam, 1984."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827598347411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:28Z","timestamp":1787334688000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827598347411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":12,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827598347411"],"URL":"https:\/\/doi.org\/10.1137\/s1064827598347411","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}