{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:55:55Z","timestamp":1776790555224,"version":"3.51.2"},"reference-count":27,"publisher":"American Mathematical Society (AMS)","issue":"267","license":[{"start":{"date-parts":[[2010,2,18]],"date-time":"2010-02-18T00:00:00Z","timestamp":1266451200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We propose fully discrete schemes to approximate the harmonic map heat flow and wave maps into spheres. The finite-element based schemes preserve a unit length constraint at the nodes by means of approximate discrete Lagrange multipliers, satisfy a discrete energy law, and iterates are shown to converge to weak solutions of the continuous problem. Comparative computational studies are included to motivate finite-time blow-up behavior in both cases.<\/p>","DOI":"10.1090\/s0025-5718-09-02221-2","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1269-1292","source":"Crossref","is-referenced-by-count":22,"title":["Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers"],"prefix":"10.1090","volume":"78","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[]},{"given":"Christian","family":"Lubich","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,18]]},"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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