{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:54:55Z","timestamp":1776844495662,"version":"3.51.2"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,5,16]],"date-time":"2013-05-16T00:00:00Z","timestamp":1368662400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2014,2]]},"DOI":"10.1007\/s10444-013-9305-4","type":"journal-article","created":{"date-parts":[[2013,5,15]],"date-time":"2013-05-15T08:09:44Z","timestamp":1368605384000},"page":"201-244","source":"Crossref","is-referenced-by-count":2,"title":["A newton-penalty method for a simplified liquid crystal model"],"prefix":"10.1007","volume":"40","author":[{"given":"Qiya","family":"Hu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Long","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,5,16]]},"reference":[{"key":"9305_CR1","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1137\/S0036142994264249","volume":"34","author":"F Alouges","year":"1997","unstructured":"Alouges, F.: A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. SIAM J. Numer. Anal. 34, 1708\u20131726 (1997)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9305_CR2","first-page":"187196","volume":"S1","author":"F Alouges","year":"2008","unstructured":"Alouges, F.: A new finite element scheme for Landau-Lifchitz equations. Discret. Contin. Dyn. Syst. Ser. S1(2), 187196 (2008)","journal-title":"Discret. Contin. Dyn. Syst. Ser."},{"key":"9305_CR3","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1137\/040606594","volume":"43","author":"S Bartels","year":"2005","unstructured":"Bartels, S.: Stability and convergence of finite element approximation schemes for harmonic maps. SIAM J. Numer. Anal. 43, 220\u2013238 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"9305_CR4","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1090\/S0025-5718-09-02300-X","volume":"79","author":"S Bartels","year":"2010","unstructured":"Bartels, S.: Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces. Math. Comp. 79, 1263\u20131301 (2010)","journal-title":"Math. Comp."},{"issue":"4","key":"9305_CR5","doi-asserted-by":"crossref","first-page":"1471C1498","DOI":"10.1137\/070680825","volume":"40","author":"J Barrett","year":"2008","unstructured":"Barrett, J., Feng, X., Prohl, A.: On p-harmonic map heat flows for 1 \u2264 p < \u221e and their finite element approximations. SIAM J. Math. Anal. 40(4), 1471C1498 (2008)","journal-title":"SIAM J. Math. Anal."},{"key":"9305_CR6","volume-title":"Ginzburg-Landau vortices. Progress in Nonlinear Differential Equations and their Applications, vol. 13","author":"F Bethuel","year":"1994","unstructured":"Bethuel, F., Brezis, H., H\u0301elein, F.: Ginzburg-Landau vortices. Progress in Nonlinear Differential Equations and their Applications, vol. 13. Birkhauser Boston, Inc, Boston (1994)"},{"key":"9305_CR7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1090\/S0273-0979-03-00976-5","volume":"40","author":"H Brezis","year":"2003","unstructured":"Brezis, H.: The interplay between analysis and topology in some nonlinear PDE problems. Bull. Amer. Math. Soc. 40, 179\u2013201 (2003)","journal-title":"Bull. Amer. Math. Soc."},{"key":"9305_CR8","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BF01161997","volume":"201","author":"Y Chen","year":"1989","unstructured":"Chen, Y., Struwe, M.: Existence and partial regularity results for the heat flow for harmonic maps. Math. Z. 201, 83\u2013103 (1989)","journal-title":"Math. Z."},{"key":"9305_CR9","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1137\/S0036142995295789","volume":"35","author":"X Chen","year":"1998","unstructured":"Chen, X.: Global and superlinear convergence of inexact Uzawa methods for saddle-point problems with nondifferentiable mappings. SIAM J. Numer. Anal. 35, 1130\u20131148 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"9305_CR10","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1137\/S0036142999352199","volume":"38","author":"W E","year":"2000","unstructured":"E, W., Wang, X.: Numerical Methods for the Landau-Lifshitz equation. SIAM J. Numer. Anal. 38, 1647\u20131665 (2000)","journal-title":"SIAM J. Numer. Anal."},{"key":"9305_CR11","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/S0010-4655(02)00823-8","volume":"152","author":"R Glowinski","year":"2003","unstructured":"Glowinski, R., Lin, P., Pan, X.: An operator-splitting method for a liquid crystal model. Comput. Phys. Commun. 152, 242\u2013252 (2003)","journal-title":"Comput. Phys. Commun."},{"key":"9305_CR12","first-page":"591","volume":"312","author":"F H\u00e9lein","year":"1991","unstructured":"H\u00e9lein, F.: R\u00e9gularit\u00e9 des applications faiblement harmoniques une surface et une vari\u00e9t\u00e9 riemannienne. C. R. Acad. Sci. Paris 312, 591\u2013596 (1991)","journal-title":"C. R. Acad. Sci. Paris"},{"key":"9305_CR13","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543036","volume-title":"Maps harmonic conservation laws and moving frames","author":"F H\u00e9lein","year":"2002","unstructured":"H\u00e9lein, F.: Maps harmonic conservation laws and moving frames. Cambridge University Press, Cambridge (2002)"},{"key":"9305_CR14","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1137\/060675575","volume":"47","author":"Q Hu","year":"2009","unstructured":"Hu, Q., Tai, X.-C., Winther, R.: A saddle-point approach to the computation of harmonic maps. SIAM J. Numer. Anal. 47, 1500\u20131523 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"9305_CR15","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1137\/S1052623403428683","volume":"16","author":"Q Hu","year":"2006","unstructured":"Hu, Q., Zou, J.: Nonlinear Inexact Uzawa Algorithms for Linear and Nonlinear Saddle-point Problems. SIAM J. Optim. 16, 798\u2013825 (2006)","journal-title":"SIAM J. Optim."},{"key":"9305_CR16","doi-asserted-by":"crossref","unstructured":"Luo, C., Majumdar, A., Erban, R.: Multistability in planar liquid crystal wells. Phys. Rev. E 85(6) (2012)","DOI":"10.1103\/PhysRevE.85.061702"},{"issue":"1","key":"9305_CR17","first-page":"142","volume":"10","author":"Q Hu","year":"2006","unstructured":"Pierre, M.: Newton and conjugate gradient for harmonic maps from the disc into the sphere. ESAIM: Control Optimisation Calc. Var. 10(1), 142\u2013167 (2004)","journal-title":"ESAIM: Control Optimisation Calc. Var."},{"key":"9305_CR18","volume-title":"Introduction to Optimization","author":"BT Polyak","year":"1987","unstructured":"Polyak, B.T.: Introduction to Optimization. Optimization Software. Inc., Publications Division, New York (1987)"},{"issue":"1","key":"9305_CR19","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1023\/A:1013775420323","volume":"46","author":"R Vanselow","year":"2001","unstructured":"Vanselow, R.: About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the poisson equation. Appl. Math. 46(1), 13\u201328 (2001)","journal-title":"Appl. Math."},{"key":"9305_CR20","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1137\/1034116","volume":"34","author":"J Xu","year":"1992","unstructured":"Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581\u2013613 (1992)","journal-title":"SIAM Rev."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9305-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-013-9305-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-013-9305-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:17Z","timestamp":1559149697000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-013-9305-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,16]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["9305"],"URL":"https:\/\/doi.org\/10.1007\/s10444-013-9305-4","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,16]]}}}