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Before singularities appear in the limiting Euler equation, we recover the quadratic physical observables as well as the wave function with mesh size and time step independent of the Planck constant. This approach is also well suited to the linear Schr\u00f6dinger equation.<\/jats:p>","DOI":"10.1137\/120899017","type":"journal-article","created":{"date-parts":[[2013,12,5]],"date-time":"2013-12-05T12:43:37Z","timestamp":1386247417000},"page":"1228-1260","source":"Crossref","is-referenced-by-count":10,"title":["An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit"],"prefix":"10.1137","volume":"11","author":[{"given":"Christophe","family":"Besse","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R\u00e9mi","family":"Carles","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Florian","family":"M\u00e9hats","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,12,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/13.1.115"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-008-0276-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/100800373"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"H. Bahouri, J.Y. Chemin, and R. Danchin,\n                      Fourier Analysis and Nonlinear Partial Differential Equations\n                      , Grundlehren Math. Wiss. [Fundamental Principles of Mathematical Sciences] 343, Springer, Heidelberg, 2011.","DOI":"10.1007\/978-3-642-16830-7"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6956"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501393253"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.11.032"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901396521"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900381497"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1080\/03605300008821529"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.11.011"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"R. 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