{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T10:24:15Z","timestamp":1769855055272,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2002,11,1]],"date-time":"2002-11-01T00:00:00Z","timestamp":1036108800000},"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":[[2002,11]]},"DOI":"10.1007\/bf02679439","type":"journal-article","created":{"date-parts":[[2007,7,29]],"date-time":"2007-07-29T04:25:26Z","timestamp":1185683126000},"page":"109-129","source":"Crossref","is-referenced-by-count":21,"title":["On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs"],"prefix":"10.1007","volume":"93","author":[{"given":"S. H.","family":"Lui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02679439_CR1","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1137\/1018114","volume":"18","author":"H. Amann","year":"1976","unstructured":"H. Amann: Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces. SIAM Rev.18, 620\u2013709 (1976)","journal-title":"SIAM Rev."},{"key":"BF02679439_CR2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1137\/0728010","volume":"28","author":"L. Badea","year":"1991","unstructured":"L. Badea: On the schwarz alternating method with more than two subdomains for nonlinear monotone problems. SIAM J. Numer. Anal.28, 179\u2013204 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02679439_CR3","doi-asserted-by":"crossref","unstructured":"X. C. Cai, M. Dryja: Domain decomposition methods for monotone nonlinear elliptic problems. In D. Keyes, J. Xu, editors, Domain decomposition methods in scientific and engineering computing, pp. 335\u2013360, Providence, R.I., 1994. AMS","DOI":"10.1090\/conm\/180\/01953"},{"key":"BF02679439_CR4","doi-asserted-by":"crossref","unstructured":"X. C. Cai, D. E. Keyes: Nonlinearly preconditioned inexact newton algorithms. SIAM J. Sci. Comput. (to appear)","DOI":"10.1137\/S106482750037620X"},{"key":"BF02679439_CR5","doi-asserted-by":"crossref","unstructured":"T. F. Chan, T. P. Mathew: Domain decomposition algorithms. Acta Numerica, pp. 61\u2013143, 1994","DOI":"10.1017\/S0962492900002427"},{"key":"BF02679439_CR6","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1090\/S0025-5718-96-00703-X","volume":"65","author":"G. Chen","year":"1996","unstructured":"G. Chen, Y. Deng, W. M. Ni, J. Zhou: Boundary element monotone iteration scheme for semilinear elliptic partial differential equations. Math. Comp.65, 943\u2013982 (1996)","journal-title":"Math. Comp."},{"key":"BF02679439_CR7","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1090\/S0025-5718-99-01109-6","volume":"69","author":"G. Chen","year":"2000","unstructured":"G. Chen, Y. Deng, W. M. Ni, J. Zhou: Boundary element monotone iteration scheme for semilinear elliptic partial differential equations part ii. Math. Comp.69, 629\u2013652 (2000)","journal-title":"Math. Comp."},{"key":"BF02679439_CR8","doi-asserted-by":"crossref","unstructured":"M. Dryja, W. Hackbusch: On the nonlinear domain decomposition method. BIT, pp. 296\u2013311, 1997","DOI":"10.1007\/BF02510214"},{"key":"BF02679439_CR9","unstructured":"M. Dryja, O. B. Widlund: An additive variant of the Schwarz alternating method for the case of many subregions. Technical report, Courant Institute Technical Report 339, 1987"},{"key":"BF02679439_CR10","volume-title":"First Int. Symp. on Domain Decomposition Methods","author":"R. Glowinski","year":"1988","unstructured":"R. Glowinski, G. H. Golub, G. A. Meurant, J. Periaux: First Int. Symp. on Domain Decomposition Methods. SIAM, Philadelphia, 1988"},{"key":"BF02679439_CR11","first-page":"1571","volume":"47","author":"C. Gui","year":"1994","unstructured":"C. Gui, Y. Lou: Uniqueness and nonuniqueness of coexistence states in the lotkavolterra competition model. CPAM47, 1571\u20131594 (1994)","journal-title":"CPAM"},{"key":"BF02679439_CR12","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1090\/conm\/218\/3020","volume-title":"Domain Decomposition Methods 10","author":"D. K. Kaushik","year":"1998","unstructured":"D. K. Kaushik, D. E. Keyes, B. F. Smith: On the interaction of architecture and algorithm in the domain-based parallelization of an unstructured-grid incompressible flow code. In J. Mandel, C. Farhat, X. C. Cai, editors, Domain Decomposition Methods 10, pp. 287\u2013295, Providence, 1998. AMS"},{"issue":"12","key":"BF02679439_CR13","first-page":"1361","volume":"16","author":"H.B. Keller","year":"1967","unstructured":"H.B. Keller, D.S. Cohen: Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16(12):1361\u20131376, 1967","journal-title":"J. Math. Mech."},{"key":"BF02679439_CR14","first-page":"1","volume-title":"First Int. Symp. on Domain Decomposition Methods","author":"P. L. Lions","year":"1988","unstructured":"P. L. Lions: On the Schwarz alternating method I. In R. Glowinski, G. H. Golub, G. A. Meurant, J. Periaux, editors, First Int. Symp. on Domain Decomposition Methods, pp. 1\u201342, Philadelphia, 1988. SIAM"},{"key":"BF02679439_CR15","first-page":"47","volume-title":"Second Int. Conference on Domain Decomposition Methods","author":"P. L. Lions","year":"1989","unstructured":"P. L. Lions: On the Schwarz alternating method II. In T. F. Chan, R. Glowinski, J. Periaux, O. Widlund, editors, Second Int. Conference on Domain Decomposition Methods, pp. 47\u201370, Philadelphia, 1989. SIAM"},{"key":"BF02679439_CR16","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1137\/S1064827597327553","volume":"21","author":"S. H. Lui","year":"2000","unstructured":"S. H. Lui: On Schwarz alternating methods for nonlinear elliptic pdes. SIAM J. Sci. Comput.21, 1506\u20131523 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"BF02679439_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/m2an:2001104","volume":"35","author":"S. H. Lui","year":"2001","unstructured":"S. H. Lui: On monotone and Schwarz alternating methods for nonlinear elliptic PDEs. M2AN35, 1\u201315 (2001)","journal-title":"M2AN"},{"key":"BF02679439_CR18","doi-asserted-by":"crossref","first-page":"1974","DOI":"10.1137\/S1064827598347411","volume":"22","author":"S. H. Lui","year":"2001","unstructured":"S. H. Lui: On Schwarz alternating methods for the incompressible Navier-Stokes equations. SIAM J. Sci. Comput.22, 1974\u20131986 (2001)","journal-title":"SIAM J. Sci. Comput."},{"key":"BF02679439_CR19","volume-title":"Nonlinear Parabolic and Elliptic Equations","author":"C. V. Pao","year":"1992","unstructured":"C. V. Pao: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, 1992"},{"key":"BF02679439_CR20","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s002110050168","volume":"72","author":"C. V. Pao","year":"1995","unstructured":"C. V. Pao: Block monotone iterative methods for numerical solutions of nonlinear elliptic equations. Numer. Math.72, 239\u2013262 (1995)","journal-title":"Numer. Math."},{"key":"BF02679439_CR21","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198501787.001.0001","volume-title":"Domain Decomposition Methods for Partial Differential Equations","author":"A. Quarteroni","year":"1999","unstructured":"A. Quarteroni, A. Valli: Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, Oxford, 1999"},{"key":"BF02679439_CR22","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1512\/iumj.1972.21.21079","volume":"21","author":"D. H. Sattinger","year":"1972","unstructured":"D. H. Sattinger: Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J.21, 979\u20131000 (1972)","journal-title":"Indiana Univ. Math. J."},{"key":"BF02679439_CR23","volume-title":"Domain Decomposition: Parallel Multilevel Algorithms for Elliptic Partial Differential Equations","author":"B. F. Smith","year":"1996","unstructured":"B. F. Smith, P. Bjorstad, W. D. Gropp: Domain Decomposition: Parallel Multilevel Algorithms for Elliptic Partial Differential Equations. Camdridge University Press, New York, 1996"},{"key":"BF02679439_CR24","first-page":"335","volume-title":"Domain decomposition methods in scientific and engineering computing","author":"X. C. Tai","year":"1994","unstructured":"X. C. Tai: Domain decomposition for linear and nonlinear elliptic problems via function or space decomposition. In D. Keyes, J. Xu, editors, Domain decomposition methods in scientific and engineering computing, pp. 335\u2013360, Providence, R.I., 1994. AMS"},{"key":"BF02679439_CR25","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1137\/S0036142996297461","volume":"35","author":"X. C. Tai","year":"1998","unstructured":"X. C. Tai, M. Espedal: Rate of convergence of some space decomposition methods for linear and nonlinear problems. SIAM J. Numer. Anal.35, 1558\u20131570 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02679439_CR26","doi-asserted-by":"crossref","unstructured":"X. C. Tai, J. Xu: Global convergence of subspace correction methods for convex optimization problems. Math. Comp. (to appear)","DOI":"10.1090\/S0025-5718-01-01311-4"},{"key":"BF02679439_CR27","first-page":"121","volume":"1","author":"P. Tallec Le","year":"1994","unstructured":"P. Le Tallec: Domain decomposition methods in computational mechanics. Computational Mechanics Advances1, 121\u2013220 (1994)","journal-title":"Computational Mechanics Advances"},{"key":"BF02679439_CR28","doi-asserted-by":"crossref","first-page":"1759","DOI":"10.1137\/S0036142992232949","volume":"33","author":"J. Xu","year":"1996","unstructured":"J. Xu: Two-grid discretization techniques for linear and nonlinear PDEs. SIAM J. Numer. Anal.33, 1759\u20131777 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02679439_CR29","first-page":"47","volume":"10","author":"J. Zou","year":"1992","unstructured":"J. Zou, H.-C. Huang: Algebriac subproblem decomposition methods and parallel algorithms with monotone convergence. J. Comput. Math.10, 47\u201359 (1992)","journal-title":"J. Comput. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02679439.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02679439\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02679439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,17]],"date-time":"2024-02-17T04:00:51Z","timestamp":1708142451000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02679439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,11]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,11]]}},"alternative-id":["BF02679439"],"URL":"https:\/\/doi.org\/10.1007\/bf02679439","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,11]]}}}