{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T05:34:38Z","timestamp":1784784878737,"version":"3.55.0"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"262","license":[{"start":{"date-parts":[[2008,10,29]],"date-time":"2008-10-29T00:00:00Z","timestamp":1225238400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The Landau-Lifshitz-Gilbert equation describes magnetic behavior in ferromagnetic materials. Construction of numerical strategies to approximate weak solutions for this equation is made difficult by its top order nonlinearity and nonconvex constraint. In this paper, we discuss necessary scaling of numerical parameters and provide a refined convergence result for the scheme first proposed by Alouges and Jaisson (2006). As an application, we numerically study discrete finite time blowup in two dimensions.<\/p>","DOI":"10.1090\/s0025-5718-07-02079-0","type":"journal-article","created":{"date-parts":[[2008,1,15]],"date-time":"2008-01-15T12:55:08Z","timestamp":1200401708000},"page":"773-788","source":"Crossref","is-referenced-by-count":56,"title":["Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation"],"prefix":"10.1090","volume":"77","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joy","family":"Ko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2007,10,29]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1142\/S0218202506001169","article-title":"Convergence of a finite element discretization for the Landau-Lifshitz equations in micromagnetism","volume":"16","author":"Alouges, Fran\u00e7ois","year":"2006","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"11","key":"2","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1016\/0362-546X(92)90196-L","article-title":"On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness","volume":"18","author":"Alouges, Fran\u00e7ois","year":"1992","journal-title":"Nonlinear Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0362-546X","issn-type":"print"},{"key":"3","doi-asserted-by":"crossref","unstructured":"John W. Barrett, S\u00f6ren Bartels, Xiaobing Feng, and Andreas Prohl. A convergent and constraint-preserving finite finite element method for the \ud835\udc5d-harmonic flow into spheres. SIAM J. Numer. Anal. (accepted), 2006.","DOI":"10.1137\/050639429"},{"issue":"2","key":"4","first-page":"507","article-title":"Finite-time blow-up of the heat flow of harmonic maps from surfaces","volume":"36","author":"Chang, Kung-Ching","year":"1992","journal-title":"J. Differential Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-040X","issn-type":"print"},{"issue":"4","key":"5","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/S0294-1449(16)30295-5","article-title":"Nonuniqueness for the heat flow of harmonic maps","volume":"7","author":"Coron, J.-M.","year":"1990","journal-title":"Ann. Inst. H. Poincar\\'{e} C Anal. Non Lin\\'{e}aire","ISSN":"https:\/\/id.crossref.org\/issn\/0294-1449","issn-type":"print"},{"issue":"5","key":"6","doi-asserted-by":"publisher","first-page":"1647","DOI":"10.1137\/S0036142999352199","article-title":"Numerical methods for the Landau-Lifshitz equation","volume":"38","author":"E, Weinan","year":"2000","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"7","doi-asserted-by":"crossref","unstructured":"Josef Fidler and Thomas Schrefl. Micromagnetic modelling \u2014 the current state of the art. 33:R135\u2013R156, 2000.","DOI":"10.1088\/0022-3727\/33\/15\/201"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/BF01191298","article-title":"The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps","volume":"1","author":"Guo, Bo Ling","year":"1993","journal-title":"Calc. Var. Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0944-2669","issn-type":"print"},{"issue":"4","key":"9","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1002\/cpa.20143","article-title":"Schr\u00f6dinger flow near harmonic maps","volume":"60","author":"Gustafson, S.","year":"2007","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"issue":"6","key":"10","doi-asserted-by":"publisher","first-page":"2681","DOI":"10.1088\/0951-7715\/18\/6\/014","article-title":"The construction of a partially regular solution to the Landau-Lifshitz-Gilbert equation in \u211d\u00b2","volume":"18","author":"Ko, Joy","year":"2005","journal-title":"Nonlinearity","ISSN":"https:\/\/id.crossref.org\/issn\/0951-7715","issn-type":"print"},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1137\/S0036144504446187","article-title":"Recent developments in the modeling, analysis, and numerics of ferromagnetism","volume":"48","author":"Kru\u017e\u00edk, Martin","year":"2006","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"issue":"2","key":"12","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s00526-003-0253-6","article-title":"Logarithmic lower bounds for N\u00e9el walls","volume":"21","author":"Melcher, Christof","year":"2004","journal-title":"Calc. Var. Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0944-2669","issn-type":"print"},{"issue":"2","key":"13","first-page":"803","article-title":"Numerical study of the appearance of singularities in ferromagnets","volume":"12","author":"Pistella, F.","year":"2002","journal-title":"Adv. Math. Sci. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1343-4373","issn-type":"print"},{"issue":"2","key":"14","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s00220-005-1490-7","article-title":"Schr\u00f6dinger maps and anti-ferromagnetic chains","volume":"262","author":"Shatah, Jalal","year":"2006","journal-title":"Comm. Math. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3616","issn-type":"print"},{"issue":"4","key":"15","doi-asserted-by":"publisher","first-page":"558","DOI":"10.1007\/BF02567432","article-title":"On the evolution of harmonic mappings of Riemannian surfaces","volume":"60","author":"Struwe, Michael","year":"1985","journal-title":"Comment. Math. Helv.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-2571","issn-type":"print"},{"issue":"1","key":"16","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1006\/jcph.2001.6793","article-title":"A Gauss-Seidel projection method for micromagnetics simulations","volume":"171","author":"Wang, Xiao-Ping","year":"2001","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02079-0\/S0025-5718-07-02079-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02079-0\/S0025-5718-07-02079-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:09Z","timestamp":1776784689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-262\/S0025-5718-07-02079-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10,29]]},"references-count":16,"journal-issue":{"issue":"262","published-print":{"date-parts":[[2008,4]]}},"alternative-id":["S0025-5718-07-02079-0"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-07-02079-0","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2007,10,29]]}}}