{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T09:50:33Z","timestamp":1770976233751,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2005,7,5]],"date-time":"2005-07-05T00:00:00Z","timestamp":1120521600000},"content-version":"vor","delay-in-days":4480,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Methods in Fluids"],"published-print":{"date-parts":[[1993,3,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A two\u2010dimensional (in\u2010plane) numerical model for surface waves propagation based on the non\u2010linear dispersive wave approach described by Boussinesq\u2010type equations, which provide an attractive theory for predicting the depth\u2010averaged velocity field resulting from that wave\u2010type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite\u2010difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.<\/jats:p>","DOI":"10.1002\/fld.1650160602","type":"journal-article","created":{"date-parts":[[2005,8,9]],"date-time":"2005-08-09T08:29:02Z","timestamp":1123576142000},"page":"447-459","source":"Crossref","is-referenced-by-count":43,"title":["Surface waves propagation in shallow water: A finite element model"],"prefix":"10.1002","volume":"16","author":[{"given":"J. S. Antunes","family":"Do Carmo","sequence":"first","affiliation":[]},{"given":"F. J. Seabra","family":"Santos","sequence":"additional","affiliation":[]},{"given":"E.","family":"Barth\u00e9lemy","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,7,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9429(1989)115:7(950)"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9429(1991)117:9(1195)"},{"key":"e_1_2_1_4_2","first-page":"815","article-title":"Run\u2010up of solitary waves","volume":"27","author":"Pedersen G.","year":"1983","journal-title":"J. Fluid Mech."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112066001678"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112067002605"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-950X(1987)113:4(327)"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620110806"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620100209"},{"issue":"17","key":"e_1_2_1_10_2","first-page":"55","article-title":"Th\u00e9orie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal","volume":"2","author":"Boussinesq J.","year":"1872","journal-title":"L. Math. Pure et Appl."},{"issue":"6","key":"e_1_2_1_11_2","first-page":"671","article-title":"\u00c9tude th\u00e9orique et exp\u00e9rimentale des domaines de validit\u00e9 des th\u00e9ories d'\u00e9volution des ondes en eau peu profonde","volume":"6","author":"Santos F. J. Seabra","year":"1988","journal-title":"Ann. Geophys."},{"key":"e_1_2_1_12_2","unstructured":"F. J. SeabraSantos \u2018Wu and Green & Naghdi approximations in the framework of the shallow\u2010water theory\u2019 4\u00b0 Simp\u00f3sio Luso\u2010Brasileiro de Hidr\u00e1ulica e Recursos Hidricos LNEC Lisboa Portugal."}],"container-title":["International Journal for Numerical Methods in Fluids"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Ffld.1650160602","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/fld.1650160602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T04:15:28Z","timestamp":1698207328000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/fld.1650160602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3,30]]},"references-count":11,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1993,3,30]]}},"alternative-id":["10.1002\/fld.1650160602"],"URL":"https:\/\/doi.org\/10.1002\/fld.1650160602","archive":["Portico"],"relation":{},"ISSN":["0271-2091","1097-0363"],"issn-type":[{"value":"0271-2091","type":"print"},{"value":"1097-0363","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3,30]]}}}