{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T09:53:46Z","timestamp":1776765226828,"version":"3.51.2"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"216","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper we prove a double order for the convergence of eigenfrequencies in fluid-structure vibration problems. We improve estimates given recently for compressible and incompressible fluids. To do this, we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators.<\/p>","DOI":"10.1090\/s0025-5718-96-00739-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1463-1475","source":"Crossref","is-referenced-by-count":22,"title":["The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems"],"prefix":"10.1090","volume":"65","author":[{"given":"Rodolfo","family":"Rodr\u00edguez","sequence":"first","affiliation":[]},{"given":"Jorge","family":"Solomin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"I. Babu\u0161ka and J. Osborn,  Eigenvalue problems, in Handbook of Numerical Analysis, Vol. II (ed. P. G. Ciarlet and J. L. Lions) North Holland, Amsterdam, 1991.","DOI":"10.1016\/S1570-8659(05)80042-0"},{"key":"2","doi-asserted-by":"crossref","unstructured":"A. Berm\u00fadez, R. Dur\u00e1n, M.A. Muschietti, R. Rodr\u00edguez and J. Solomin,  Finite element vibration analysis of fluid-solid systems without spurious modes, SIAM J. Numer. Anal., 32 (1995), 1280\u20131295.","DOI":"10.1137\/0732059"},{"key":"3","unstructured":"A. Berm\u00fadez, R. Dur\u00e1n and R. Rodr\u00edguez,  Finite element analysis of compressible and incompressible fluid-solid systems, Math. Comp. (submitted)"},{"key":"4","unstructured":"A. Berm\u00fadez, R. Dur\u00e1n and R. Rodr\u00edguez,  Finite element solution of incompressible fluid-structure vibration problems, Internat. J. Numer. Methods Engrg. (submitted)"},{"issue":"3-4","key":"5","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/0045-7825(94)90095-7","article-title":"Finite element computation of the vibration modes of a fluid-solid system","volume":"119","author":"Berm\u00fadez, Alfredo","year":"1994","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"2","key":"6","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1051\/m2an\/1987210202391","article-title":"Mathematical formulation of fluid-structure interaction problems","volume":"21","author":"Boujot, Jacqueline","year":"1987","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"key":"7","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3172-1","volume-title":"Mixed and hybrid finite element methods","volume":"15","author":"Brezzi, Franco","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0387975829"},{"key":"8","doi-asserted-by":"crossref","unstructured":"H. C. Chen and R. L. Taylor,  Vibration analysis of fluid-solid systems using a finite element displacement formulation, Internat. J. Numer. Meth. Eng., 29 (1990) 683-698.","DOI":"10.1002\/nme.1620290402"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1051\/m2an\/1978120200971","article-title":"On spectral approximation. I. The problem of convergence","volume":"12","author":"Descloux, Jean","year":"1978","journal-title":"RAIRO Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0399-0516","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1002\/sapm1939181153","article-title":"A function related to the series for \ud835\udc52^{\ud835\udc52^{\ud835\udc65}}","volume":"18","author":"Epstein, Leo F.","year":"1939","journal-title":"J. Math. Phys. Mass. Inst. Tech.","ISSN":"https:\/\/id.crossref.org\/issn\/0097-1421","issn-type":"print"},{"key":"11","doi-asserted-by":"crossref","unstructured":"M. Hamdi, Y. Ouset and G. Verchery,  A displacement method for the analysis of vibrations of coupled fluid-structure systems, Internat. J. Numer. Methods Eng., 13 (1978) 139-150.","DOI":"10.1002\/nme.1620130110"},{"key":"12","series-title":"Recherches en Math\\'{e}matiques Appliqu\\'{e}es [Research in Applied Mathematics]","isbn-type":"print","volume-title":"Interactions fluides-structures","volume":"23","author":"Morand, Henri J.-P.","year":"1992","ISBN":"https:\/\/id.crossref.org\/isbn\/2225827885"},{"issue":"154","key":"13","doi-asserted-by":"publisher","first-page":"427","DOI":"10.2307\/2007651","article-title":"Eigenvalue approximation by mixed and hybrid methods","volume":"36","author":"Mercier, B.","year":"1981","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"14","doi-asserted-by":"crossref","unstructured":"L. Olson and K. Bathe,  Analysis of fluid-structure interactions. A direct symmetric coupled formulation based on the fluid velocity potential, Comp. Struct., 21 (1985) 21-32.","DOI":"10.1016\/0045-7949(85)90226-3"},{"key":"15","first-page":"292","article-title":"A mixed finite element method for 2nd order elliptic problems","author":"Raviart, P.-A.","year":"1977"},{"key":"16","unstructured":"J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00739-9\/S0025-5718-96-00739-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00739-9\/S0025-5718-96-00739-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:16:29Z","timestamp":1776719789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-216\/S0025-5718-96-00739-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":16,"journal-issue":{"issue":"216","published-print":{"date-parts":[[1996,10]]}},"alternative-id":["S0025-5718-96-00739-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00739-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1996]]}}}