{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:54:30Z","timestamp":1776840870690,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"243","license":[{"start":{"date-parts":[[2003,12,3]],"date-time":"2003-12-03T00:00:00Z","timestamp":1070409600000},"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>\n                    This paper deals with the finite element approximation of the spectral problem for the Laplace equation with Neumann boundary conditions on a curved nonconvex domain\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"normal\">\n                            \u03a9\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Convergence and optimal order error estimates are proved for standard piecewise linear continuous elements on a discrete polygonal domain\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega Subscript h Baseline not-a-subset-of normal upper Omega\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi mathvariant=\"normal\">\n                                \u03a9\n                                \n                              <\/mml:mi>\n                              <mml:mi>h<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>\u2284<\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u03a9\n                              \n                            <\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega _h\\not \\subset \\Omega<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in the framework of the abstract spectral approximation theory.\n                  <\/p>","DOI":"10.1090\/s0025-5718-02-01467-9","type":"journal-article","created":{"date-parts":[[2003,4,18]],"date-time":"2003-04-18T13:09:02Z","timestamp":1050671342000},"page":"1099-1115","source":"Crossref","is-referenced-by-count":6,"title":["Finite element approximation of spectral problems with Neumann boundary conditions on curved domains"],"prefix":"10.1090","volume":"72","author":[{"given":"Erwin","family":"Hern\u00e1ndez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rodolfo","family":"Rodr\u00edguez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2002,12,3]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"I. Babu\u0161ka and J. Osborn, Eigenvalue problems in Handbook of Numerical Analysis, Vol II, P.G. Ciarlet and J.L. Lions, eds., North Holland, Amsterdam, 1991, pp. 641\u2013787.","DOI":"10.1016\/S1570-8659(05)80042-0"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"1212","DOI":"10.1137\/0726068","article-title":"Optimal finite-element interpolation on curved domains","volume":"26","author":"Bernardi, Christine","year":"1989","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"229","key":"3","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1090\/S0025-5718-99-01072-8","article-title":"On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form","volume":"69","author":"Boffi, Daniele","year":"2000","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1-2","key":"4","first-page":"131","article-title":"On the convergence of eigenvalues for mixed formulations","volume":"25","author":"Boffi, Daniele","year":"1997","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)","ISSN":"https:\/\/id.crossref.org\/issn\/0391-173X","issn-type":"print"},{"key":"5","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0387941932"},{"issue":"207","key":"6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2153559","article-title":"A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries","volume":"63","author":"Bramble, James H.","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"7","series-title":"Handbook of Numerical Analysis, II","isbn-type":"print","volume-title":"Handbook of numerical analysis. Vol. II","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0444703659"},{"key":"8","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0045-7825(72)90006-0","article-title":"Interpolation theory over curved elements, with applications to finite element methods","volume":"1","author":"Ciarlet, P. G.","year":"1972","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"150","key":"9","doi-asserted-by":"publisher","first-page":"441","DOI":"10.2307\/2006095","article-title":"Polynomial approximation of functions in Sobolev spaces","volume":"34","author":"Dupont, Todd","year":"1980","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1-2","key":"10","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1080\/01630568908816293","article-title":"On the finite element approximation of functions with noninteger derivatives","volume":"10","author":"Feistauer, M.","year":"1989","journal-title":"Numer. Funct. Anal. Optim.","ISSN":"https:\/\/id.crossref.org\/issn\/0163-0563","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/BF01396664","article-title":"Finite element solution of nonlinear elliptic problems","volume":"50","author":"Feistauer, Miloslav","year":"1987","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"12","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite element methods for Navier-Stokes equations","volume":"5","author":"Girault, Vivette","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/3540157964"},{"key":"13","series-title":"Monographs and Studies in Mathematics","isbn-type":"print","volume-title":"Elliptic problems in nonsmooth domains","volume":"24","author":"Grisvard, P.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0273086472"},{"issue":"207","key":"14","doi-asserted-by":"publisher","first-page":"19","DOI":"10.2307\/2153560","article-title":"Error estimate in an isoparametric finite element eigenvalue problem","volume":"63","author":"Lebaud, M.-P.","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"15","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1090\/S0025-5718-1975-0383117-3","article-title":"Spectral approximation for compact operators","volume":"29","author":"Osborn, John E.","year":"1975","journal-title":"Math. Comput."},{"key":"16","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":"17","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1137\/0712032","article-title":"Interpolated boundary conditions in the finite element method","volume":"12","author":"Scott, Ridgway","year":"1975","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"18","series-title":"Prentice-Hall Series in Automatic Computation","volume-title":"An analysis of the finite element method","author":"Strang, Gilbert","year":"1973"},{"issue":"5","key":"19","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1051\/m2an\/1993270505651","article-title":"External finite element approximations of eigenvalue problems","volume":"27","author":"Vanmaele, M.","year":"1993","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. Num\\'{e}r.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"1-3","key":"20","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"},{"issue":"2","key":"21","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s002110050144","article-title":"The combined effect of numerical integration and approximation of the boundary in the finite element method for eigenvalue problems","volume":"71","author":"Vanmaele, Mich\u00e8le","year":"1995","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"22","series-title":"Computational Mathematics and Applications","isbn-type":"print","volume-title":"Nonlinear elliptic and evolution problems and their finite element approximations","author":"\u017den\u00ed\u0161ek, A.","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/012779560X"},{"key":"23","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1137\/0710022","article-title":"Curved elements in the finite element method. I","volume":"10","author":"Zl\u00e1mal, Milo\u0161","year":"1973","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01467-9\/S0025-5718-02-01467-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01467-9\/S0025-5718-02-01467-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:19:52Z","timestamp":1776727192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01467-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12,3]]},"references-count":23,"journal-issue":{"issue":"243","published-print":{"date-parts":[[2003,7]]}},"alternative-id":["S0025-5718-02-01467-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-02-01467-9","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":[[2002,12,3]]}}}