{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:44:18Z","timestamp":1787334258729,"version":"build-2736575974"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>We consider a mechanical system with impact and one degree of freedom. The system is not necessarily Lagrangian. The representative point is subject to the constraint $u(t) \\in \\Er^+$ for all t. We assume that, at impact, the velocity is reversed and multiplied by a given coefficient of restitution $e\\in[0,1]$. We define a numerical scheme which enables us to approximate the solutions of the Cauchy problem: this is an ad hoc scheme which does not require a systematic search for the times of impact. We prove the convergence of this numerical scheme to a solution. Many of the features of this proof will be reused in the nonconvex, multidimensional case, written in generalized coordinates, given in the companion paper [L. Paoli and M. Schatzman, SIAM J. Numer. Anal., 40 (2002), pp. 734--768]. We present some numerical results obtained with the scheme for a spring-dashpot system and we compare them to the results obtained by impact detection and penalization.<\/jats:p>","DOI":"10.1137\/s0036142900378728","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"702-733","source":"Crossref","is-referenced-by-count":96,"title":["A Numerical Scheme for Impact Problems I: The One-Dimensional Case"],"prefix":"10.1137","volume":"40","author":[{"given":"Laetitia","family":"Paoli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michelle","family":"Schatzman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","volume-title":"Analyse fonctionnelle","author":"Brezis Ha\u00efm","year":"1983"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(83)90035-9"},{"key":"R3","unstructured":"N. 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