{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T07:25:36Z","timestamp":1789716336937,"version":"4.0.1"},"reference-count":29,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this paper, a FETI-DP formulation for three dimensional elasticity on nonmatching grids over geometrically nonconforming subdomain partitions is considered. To resolve the nonconformity of the finite elements, a mortar matching condition is imposed on the subdomain interfaces (faces). A FETI-DP algorithm is then built by enforcing the mortar matching condition in dual and primal ways. In order to make the FETI-DP algorithm scalable, a set of primal constraints, which include average and momentum constraints over interfaces, are selected from the mortar matching condition. A condition number bound, $C(1+\\log(H\/h))^2$, is then proved for the FETI-DP formulation for the elasticity problems with discontinuous material parameters. Only some faces need to be chosen as primal faces on which the average and momentum constraints are imposed. Numerical results are included.<\/jats:p>","DOI":"10.1137\/060663179","type":"journal-article","created":{"date-parts":[[2008,5,16]],"date-time":"2008-05-16T18:04:06Z","timestamp":1210961046000},"page":"2346-2370","source":"Crossref","is-referenced-by-count":22,"title":["A FETI-DP Formulation of Three Dimensional Elasticity Problems with Mortar Discretization"],"prefix":"10.1137","volume":"46","author":[{"given":"Hyea Hyun","family":"Kim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,5,16]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050468"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1997310202891"},{"key":"R3","unstructured":"C. Bernardi, Y. Maday, and A. T. Patera,\n                      A new nonconforming approach to domain decomposition: The mortar element method\n                      , in Nonlinear Partial Differential Equations and Their Applications, Coll\u00e8ge de France Seminar, Vol. XI (Paris, 1989\u20131991), Pitman Res. Notes Math. Ser. 299, Longman Sci. Tech., Harlow, 1994, pp. 13\u201351."},{"key":"R4","unstructured":"D. Braess,\n                      Finite Elements\n                      , Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, 1997; translated from the 1992 German original by Larry L. Schumaker."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.03.008"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0731086"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"M. Dryja and O. B. Widlund,\n                      A FETI-DP method for a mortar discretization of elliptic problems\n                      , in Recent Developments in Domain Decomposition Methods (Z\u00fcrich, 2001), Lect. Notes Comput. Sci. Eng. 23, Springer, Berlin, 2002, pp. 41\u201352.","DOI":"10.1007\/978-3-642-56118-4_3"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"M. Dryja and O. B. Widlund,\n                      A generalized FETI-DP method for a mortar discretization of elliptic problems\n                      , in Domain Decomposition Methods in Science and Engineering (Cocoyoc, Mexico, 2002), UNAM, Mexico City, 2003, pp. 27\u201338.","DOI":"10.1007\/978-3-642-56118-4_3"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1002\/nme.76"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<687::AID-NLA219>3.0.CO;2-S"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00146-1"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620320604"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900367065"},{"key":"R14","first-page":"103","volume":"26","author":"Kim H. H.","year":"2007","journal-title":"Electron. Trans. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1097-4067","issn-type":"print"},{"key":"R15","unstructured":"H. H. Kim, M. Dryja, and O. B. Widlund,\n                      A BDDC algorithm for problems with mortar discretization using a transformation of basis\n                      , SIAM J. Numer. Anal., submitted."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903423381"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/030601119"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/050624364"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.03.023"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"A. Klawonn and O. Rheinbach,\n                      Some computational results for robust FETI-DP methods applied to heterogeneous elasticity problems in 3D\n                      , in Domain Decomposition Methods in Science and Engineering XVI, Lect. Notes Comput. Sci. Eng. 55, Springer, Berlin, 2007, pp. 389\u2013396.","DOI":"10.1007\/978-3-540-34469-8_48"},{"key":"R21","unstructured":"A. Klawonn and O. B. Widlund,\n                      Dual and dual-primal FETI methods for elliptic problems with discontinuous coefficients in three dimensions\n                      , in Domain Decomposition Methods in Sciences and Engineering (Chiba, 1999), DDM.org, Augsburg, Germany, 2001, pp. 29\u201339."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20156"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901388081"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"A. Klawonn, O. B. Widlund, and M. Dryja,\n                      Dual-primal FETI methods with face constraints\n                      , in Recent Developments in Domain Decomposition Methods (Z\u00fcrich, 2001), Lect. Notes Comput. Sci. Eng. 23, Springer, Berlin, 2002, pp. 27\u201340.","DOI":"10.1007\/978-3-642-56118-4_2"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1007\/s211-001-8014-1"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500378829"},{"key":"R27","doi-asserted-by":"crossref","unstructured":"A. Toselli and O. Widlund,\n                      Domain Decomposition Methods\u2014Algorithms and Theory\n                      , Springer Series in Computational Mathematics 34, Springer-Verlag, Berlin, 2005.","DOI":"10.1007\/b137868"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999350929"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"B. I. Wohlmuth,\n                      Discretization methods and iterative solvers based on domain decomposition\n                      , Lect. Notes Comput. Sci. Eng. 17, Springer, Berlin, 2001.","DOI":"10.1007\/978-3-642-56767-4"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060663179","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:09Z","timestamp":1787325249000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060663179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060663179"],"URL":"https:\/\/doi.org\/10.1137\/060663179","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}