{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:47Z","timestamp":1787336867607,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>A new domain decomposition method with Lagrange multipliers for elliptic problems is introduced. It is based on a reformulation of the well-known finite element tearing and interconnecting (FETI) method as a saddle point problem with both primal and dual variables as unknowns. The resulting linear system is solved with block-structured preconditioners combined with a suitable Krylov subspace method. This approach allows the use of inexact subdomain solvers for the positive definite subproblems. It is shown that the condition number of the preconditioned saddle point problem is bounded independently of the number of subregions and depends only polylogarithmically on the number of degrees of freedom of individual local subproblems. Numerical results are presented for a plane stress cantilever membrane problem.<\/jats:p>","DOI":"10.1137\/s1064827599352495","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1199-1219","source":"Crossref","is-referenced-by-count":54,"title":["A Domain Decomposition Method with Lagrange Multipliers and Inexact Solvers for Linear Elasticity"],"prefix":"10.1137","volume":"22","author":[{"given":"Axel","family":"Klawonn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olof B.","family":"Widlund","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310405171"},{"key":"R2","first-page":"129","volume":"8","author":"Brezzi F.","year":"1974","journal-title":"Rev. Fran\u00e7aise Automat. Informat. Recherche Op\u00e9rationnelle S\u00e9r. Rouge"},{"key":"R3","unstructured":"P. G. Ciarlet,\n                      Mathematical Elasticity Volume I: Three\u2010Dimensional Elasticity\n                      , North\u2013Holland, Amsterdam, 1988."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620382207"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00145-X"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(94)90068-X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320604"},{"key":"R8","first-page":"124","volume":"2","author":"Farhat Charbel","year":"1994","journal-title":"Comput. Mech. Adv."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4288-8"},{"key":"R10","unstructured":"A. Klawonn,\n                      An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term, Part II: General Theory\n                      , Technical report 14\/95, Westf\u00e4lische Wilhelms\u2010Universit\u00e4t M\u00fcnster, Germany, April 1995."},{"key":"R10","unstructured":"Also available as Technical report 683, Courant Institute of Mathematical Sciences, New York University, New York, 1995."},{"key":"R11","unstructured":"A. Klawonn,\n                      Preconditioners for Indefinite Problems\n                      , Ph.D. thesis, Westf\u00e4lische Wilhelms\u2010Universit\u00e4t M\u00fcnster, 1995;"},{"key":"R11","unstructured":"Technical report 716, Courant Institute of Mathematical Sciences, New York University, New York, 1996."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595279575"},{"key":"R13","unstructured":"A. Klawonn and O. B. Widlund,\n                      A domain decomposition method with Lagrange multipliers for linear elasticity\n                      , in Proceedings of the 11th International Conference on Domain Decomposition Methods, Greenwich, UK, 1998, C. H. Lai, P. E. Bj\u00f8rstad, M. Cross, and O. B. Widlund, eds., Domain Decomposition Press, Bergen, Norway, 1998, pp. 49\u201356. Also available online from http:\/\/www.ddm.org\/DD11\/Klawonn.ps.gz."},{"key":"R14","unstructured":"A. Klawonn and O. B. Widlund,\n                      FETI and Neumann\u2013Neumann iterative substructuring methods: Connections and new results\n                      , Comm. Pure Appl. Math., to appear."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1515\/rnam.1995.10.3.187"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050201"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997289896"},{"key":"R18","unstructured":"J. Ne\u010das,\n                      Les m\u00e9thodes directes en th\u00e9orie des \u00e9quations elliptiques\n                      , Academia, Prague, 1967."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1981150302371"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1115\/1.2789032"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19970815)40:15<2717::AID-NME185>3.0.CO;2-B"},{"key":"R22","unstructured":"D. Rixen and C. Farhat,\n                      Preconditioning the FETI and balancing domain decomposition methods for problems with intra\u2010 and inter\u2010subdomain coefficient jumps\n                      , in Proceedings of the Ninth International Conference on Domain Decomposition Methods in Science and Engineering, Bergen, Norway, 1996, P. Bj\u00f8rstad, M. Espedal, and D. Keyes, eds., Domain Decomposition Press, Bergen, Norway, 1998, pp. 472\u2013479. Also available online from http:\/\/www.ddm.org\/DD9\/Rixen.ps.gz."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19990210)44:4<489::AID-NME514>3.3.CO;2-Q"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19991010)46:4<501::AID-NME685>3.0.CO;2-7"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0613054"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0731070"},{"key":"R27","unstructured":"R. Tezaur,\n                      Analysis of Lagrange Multiplier Based Domain Decomposition\n                      , Ph.D. thesis, University of Colorado at Denver, 1998;"},{"key":"R27","unstructured":"also available online from http:\/\/www\u2010math.cudenver.edu\/graduate\/ thesis\/rtezaur.ps.gz."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599352495","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:17Z","timestamp":1787333657000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599352495"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599352495"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599352495","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}