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Discrete energy conservation laws which mimic the underlying differential conservation law are established, and convergence of all proposed methods is proved. Computational experiments are also provided to validate the proposed methods and to present numerical evidence for possible finite-time blow-ups of the wave maps.<\/jats:p>","DOI":"10.1137\/060659971","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T10:25:56Z","timestamp":1198059956000},"page":"61-87","source":"Crossref","is-referenced-by-count":18,"title":["Finite Element Approximations of Wave Maps into Spheres"],"prefix":"10.1137","volume":"46","author":[{"given":"S\u00f6ren","family":"Bartels","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobing","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,12,19]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"I. 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