{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T05:39:35Z","timestamp":1778132375998,"version":"3.51.4"},"reference-count":54,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,12,28]],"date-time":"2020-12-28T00:00:00Z","timestamp":1609113600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-16-CE92-0028"],"award-info":[{"award-number":["ANR-16-CE92-0028"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, space-varying coefficients and higher-order pHs (Euler\u2013Bernoulli beam equation) are provided.<\/jats:p>","DOI":"10.1093\/imamci\/dnaa038","type":"journal-article","created":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T22:10:54Z","timestamp":1606947054000},"page":"493-533","source":"Crossref","is-referenced-by-count":57,"title":["A partitioned finite element method for power-preserving discretization of open systems of conservation laws"],"prefix":"10.1093","volume":"38","author":[{"given":"Fl\u00e1vio Luiz","family":"Cardoso-Ribeiro","sequence":"first","affiliation":[{"name":"Divis\u00e3o de Engenharia Aeron\u00e1utica, Instituto Tecnol\u00f3gico de Aeron\u00e1utica, S\u00e3o Jos\u00e9 dos Campos, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Denis","family":"Matignon","sequence":"additional","affiliation":[{"name":"Institut Sup\u00e9rieur de l\u2019A\u00e9ronautique et de l\u2019Espace (ISAE-SUPAERO), Universit\u00e9 de Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Lef\u00e8vre","sequence":"additional","affiliation":[{"name":"Laboratoire de Conception et d\u2019Int\u00e9gration des Syst\u00e8mes (LCIS), Universit\u00e9 Grenoble Alpes, Valence, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,12,28]]},"reference":[{"key":"2021060309595096000_ref1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.jfluidstructs.2016.03.013","article-title":"A symplectic integrator for dynamic coupling between nonlinear vessel motion with variable cross-section and bottom topography and interior shallow-water sloshing","volume":"65","author":"Alemi Ardakani","year":"2016","journal-title":"J. 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