{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:49:20Z","timestamp":1776804560519,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"315","license":[{"start":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T00:00:00Z","timestamp":1554422400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-CE40- 0010"],"award-info":[{"award-number":["ANR-15-CE40- 0010"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We consider a finite-difference semi-discrete scheme for the approximation of boundary controls for the one-dimensional wave equation. The high frequency numerical spurious oscillations lead to a loss of the uniform (with respect to the mesh size) controllability property of the semi-discrete model in the natural setting. We prove that, by filtering the high frequencies of the initial data in an optimal range, we restore the uniform controllability property. Moreover, we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability. The proof is based on the moment method.<\/p>","DOI":"10.1090\/mcom\/3345","type":"journal-article","created":{"date-parts":[[2017,12,13]],"date-time":"2017-12-13T09:22:01Z","timestamp":1513156921000},"page":"273-291","source":"Crossref","is-referenced-by-count":24,"title":["Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation using a finite-difference method"],"prefix":"10.1090","volume":"88","author":[{"given":"Pierre","family":"Lissy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ionel","family":"Roven\u0163a","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2018,4,5]]},"reference":[{"issue":"301","key":"1","doi-asserted-by":"publisher","first-page":"2259","DOI":"10.1090\/mcom\/3064","article-title":"Approximation of the controls for the beam equation with vanishing viscosity","volume":"85","author":"Bugariu, Ioan Florin","year":"2016","journal-title":"Math. 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