{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T03:02:09Z","timestamp":1791082929714,"version":"4.1.0"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In a previous work [P. Crispel, P. Degond, and M.-H. Vignal, J. Comput. Phys., 223 (2007), pp. 208\u2013234], a new numerical discretization of the Euler\u2013Poisson system was proposed. This scheme is \u201casymptotic preserving\u201d in the quasineutral limit (i.e., when the Debye length $\\varepsilon$ tends to zero), which means that it becomes consistent with the limit model when $\\varepsilon \\to 0$. In the present work, we show that the stability domain of the present scheme is independent of $\\varepsilon$. This stability analysis is performed on the Fourier transformed (with respect to the space variable) linearized system. We show that the stability property is more robust when a space-decentered scheme is used (which brings in some numerical dissipation) rather than a space-centered scheme. The linearization is first performed about a zero mean velocity and then about a nonzero mean velocity. At the various stages of the analysis, our scheme is compared with more classical schemes and its improved stability property is outlined. The analysis of a fully discrete (in space and time) version of the scheme is also given. Finally, some considerations about a model nonlinear problem, the Burgers\u2013Poisson problem, are also discussed.<\/jats:p>","DOI":"10.1137\/070690584","type":"journal-article","created":{"date-parts":[[2008,3,21]],"date-time":"2008-03-21T18:06:56Z","timestamp":1206122816000},"page":"1298-1322","source":"Crossref","is-referenced-by-count":37,"title":["Analysis of an Asymptotic Preserving Scheme for the Euler\u2013Poisson System in the Quasineutral Limit"],"prefix":"10.1137","volume":"46","author":[{"given":"Pierre","family":"Degond","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian-Guo","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marie-H\u00e9l\u00e8ne","family":"Vignal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,3,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"F. 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