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\n We consider a second-order elliptic eigenvalue problem on a convex polygonal domain, divided in\n \n \n \n M<\/mml:mi>\n M<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n nonoverlapping subdomains. The conormal derivative of the unknown function is continuous on the interfaces, while the function itself is discontinuous. We present a general finite element method to obtain a numerical solution of the eigenvalue problem, starting from a nonstandard formally equivalent variational formulation in an abstract setting in product Hilbert spaces. We use standard Lagrange finite element spaces on the subdomains. Moreover, the bilinear forms are approximated by suitable numerical quadrature formulas. We obtain error estimates for both the eigenfunctions and the eigenvalues, allowing for the case of multiple exact eigenvalues, by a pure variational method.\n <\/p>","DOI":"10.1090\/s0025-5718-96-00741-7","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:13:45Z","timestamp":1027707225000},"page":"999-1017","source":"Crossref","is-referenced-by-count":4,"title":["On a variational approximation method for a class of elliptic eigenvalue problems in composite structures"],"prefix":"10.1090","volume":"65","author":[{"given":"M.","family":"Vanmaele","sequence":"first","affiliation":[]},{"given":"R.","family":"Keer","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/0377-0427(92)90016-Q","article-title":"Some results in lumped mass finite-element approximation of eigenvalue problems using numerical quadrature formulas","volume":"43","author":"Andreev, A. B.","year":"1992","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"8","key":"2","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1007\/BF01405286","article-title":"Estimation of the effect of numerical integration in finite element eigenvalue approximation","volume":"56","author":"Banerjee, Uday","year":"1990","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"3","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"key":"4","series-title":"Collection du Commissariat \\`a l'\\'{E}nergie Atomique: S\\'{e}rie Scientifique. [Collection of the Atomic Energy Commission: Science Series]","isbn-type":"print","volume-title":"Analyse math\\'{e}matique et calcul num\\'{e}rique pour les sciences et les techniques. Tome 1","author":"Dautray, Robert","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/2225804069"},{"key":"5","series-title":"Collection du Commissariat \\`a l'\\'{E}nergie Atomique: S\\'{e}rie Scientifique. [Collection of the Atomic Energy Commission: Science Series]","isbn-type":"print","volume-title":"Analyse math\\'{e}matique et calcul num\\'{e}rique pour les sciences et les techniques. Tome 2","author":"Dautray, Robert","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/222580513X"},{"key":"6","series-title":"Computer Science and Applied Mathematics","volume-title":"Methods of numerical integration","author":"Davis, Philip J.","year":"1975"},{"key":"7","unstructured":"[7] J. Ka\u010dur & R. Van Keer , On the Numerical Solution of some Heat Transfer Problems in Multi-component Structures with nonperfect Thermal Contacts. In: R.W. Lewis, (editor), Numerical Methods for Thermal Problems VII, Pineridge Press, Swansea (1991) 1378\u20131388."},{"key":"8","isbn-type":"print","volume-title":"Finite element handbook","year":"1987","ISBN":"https:\/\/id.crossref.org\/isbn\/007033305X"},{"key":"9","series-title":"Monographs and Textbooks on Mechanics of Solids and Fluids, Mechanics: Analysis","isbn-type":"print","volume-title":"Function spaces","author":"Kufner, Alois","year":"1977","ISBN":"https:\/\/id.crossref.org\/isbn\/9028600159"},{"key":"10","unstructured":"[10] M.D. Mikhailov & M.N. \u00d6zi\u015fik , Unified Analysis and Solutions of Heat and Mass Diffusion, John Wiley & Sons, N.Y. (1984)."},{"key":"11","unstructured":"[11] M.N. \u00d6zi\u015fik , Heat Conduction, (2nd edition), John Wiley & Sons, N.Y. (1993)."},{"key":"12","unstructured":"[12] A.W. Pratt , Heat Transmission in Buildings, J. Wiley, Chichester (1981)."},{"key":"13","series-title":"Collection Math\\'{e}matiques Appliqu\\'{e}es pour la Ma\\^{i}trise. [Collection of Applied Mathematics for the Master's Degree]","isbn-type":"print","volume-title":"Introduction \\`a l'analyse num\\'{e}rique des \\'{e}quations aux d\\'{e}riv\\'{e}es partielles","author":"Raviart, P.-A.","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/2225756708"},{"key":"14","unstructured":"[14] M. Vanmaele , A numerical quadrature finite element method for 2nd-order eigenvalue problems with Dirichlet-Robin boundary conditions, Proceedings ISNA\u201992, Prague (1994), 269\u2013292."},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] M. Vanmaele & R. Van Keer , Convergence and error estimates for a finite element method with numerical quadrature for a second-order elliptic eigenvalue problem, Int. Series of Num. Math., 96 (1991) 225\u2013236.","DOI":"10.1007\/978-3-0348-6332-2_17"},{"issue":"1-3","key":"16","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/0377-0427(94)90289-5","article-title":"External finite-element approximations of eigenfunctions in the case of multiple eigenvalues","volume":"50","author":"Vanmaele, M.","year":"1994","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00741-7\/S0025-5718-96-00741-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00741-7\/S0025-5718-96-00741-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:11:47Z","timestamp":1776719507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-215\/S0025-5718-96-00741-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":16,"journal-issue":{"issue":"215","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["S0025-5718-96-00741-7"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00741-7","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]]}}}