{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:25:19Z","timestamp":1787333119410,"version":"build-2736575974"},"reference-count":28,"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":[[2010,1]]},"abstract":"<jats:p>A FETI\u2013DP (dual-primal finite element tearing and interconnecting) algorithm for the three-dimensional Stokes problem is developed and analyzed. This is an extension of the previous work for the two-dimensional problem in [H. H. Kim, C.-O. Lee, and E.-H. Park, SIAM J. Numer. Anal., 47 (2010), pp. 4142\u20134162]. Advantages of this approach are the coarse problem without primal pressure unknowns and the use of a computationally cheap lumped preconditioner. Especially in three dimensions, these advantages provide a more practical FETI-DP algorithm. In three dimensions, the velocity unknowns at subdomain corners and the averages of velocity unknowns over common faces are selected as the primal unknowns in the FETI-DP formulation. Its condition number bound is analyzed to be $CH\/h$, where C is a positive constant which is independent of any mesh parameters and $H\/h$ is the number of elements across each subdomain. Numerical results are included.<\/jats:p>","DOI":"10.1137\/090777335","type":"journal-article","created":{"date-parts":[[2010,11,9]],"date-time":"2010-11-09T18:51:20Z","timestamp":1289328680000},"page":"3301-3322","source":"Crossref","is-referenced-by-count":13,"title":["A FETI\u2013DP Formulation for the Three-Dimensional Stokes Problem without Primal Pressure Unknowns"],"prefix":"10.1137","volume":"32","author":[{"given":"Hyea Hyun","family":"Kim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chang-Ock","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,11,9]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.03.012"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502412887"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1002\/nme.76"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<687::AID-NLA219>3.0.CO;2-S"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90068-X"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"V. Girault and P.A. Raviart,\n                      Finite element methods for Navier-Stokes equations, Theory and algorithms\n                      , Springer Ser. Comput. 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Li,\n                      Dual-primal FETI Methods for Stationary Stokes and Navier-Stokes Equations\n                      , Ph.D. thesis, Department of Mathematics, Courant Institute, New York University, New York, 2002."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0653-y"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/050628556"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1553"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.03.011"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1002\/nla.341"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2004.09.022"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389668"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.10020"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"A. Toselli and O. Widlund,\n                      Domain decomposition methods\u2014algorithms and theory\n                      , Springer Ser. Comput. 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