{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T02:25:54Z","timestamp":1784341554992,"version":"3.55.0"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"260","license":[{"start":{"date-parts":[[2008,5,24]],"date-time":"2008-05-24T00:00:00Z","timestamp":1211587200000},"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>Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionally converges to weak solutions of the harmonic map heat flow.<\/p>","DOI":"10.1090\/s0025-5718-07-02026-1","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T07:46:03Z","timestamp":1185435963000},"page":"1847-1859","source":"Crossref","is-referenced-by-count":41,"title":["Constraint preserving implicit finite element discretization of harmonic map flow into spheres"],"prefix":"10.1090","volume":"76","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2007,5,24]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"1708","DOI":"10.1137\/S0036142994264249","article-title":"A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case","volume":"34","author":"Alouges, Fran\u00e7ois","year":"1997","journal-title":"SIAM J. 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