{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:23:49Z","timestamp":1787315029589,"version":"build-2736575974"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"282","license":[{"start":{"date-parts":[[2013,12,12]],"date-time":"2013-12-12T00:00:00Z","timestamp":1386806400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We consider the \u201cclassical\u201d Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform horizontal channel. We discretize an initial-boundary-value problem for these systems in space using Galerkin-finite element methods and prove error estimates for the resulting semidiscrete problems and also for their fully discrete analogs effected by explicit Runge-Kutta time-stepping procedures. The theoretical orders of convergence obtained are consistent with the results of numerical experiments that are also presented.<\/p>","DOI":"10.1090\/s0025-5718-2012-02663-9","type":"journal-article","created":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T14:09:47Z","timestamp":1355321387000},"page":"689-717","source":"Crossref","is-referenced-by-count":15,"title":["Error estimates for Galerkin approximations of the \u201cclassical\u201d Boussinesq system"],"prefix":"10.1090","volume":"82","author":[{"given":"D.","family":"Antonopoulos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Dougalis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2012,12,12]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"25","DOI":"10.3934\/dcds.2011.29.25","article-title":"Existence of solutions for a Boussinesq system on the half line and on a finite interval","volume":"29","author":"Adamy, Karine","year":"2011","journal-title":"Discrete Contin. 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