{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T14:58:35Z","timestamp":1790866715458,"version":"4.1.0"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,2,4]],"date-time":"2012-02-04T00:00:00Z","timestamp":1328313600000},"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                    We propose and analyze an approximation technique for the Maxwell eigenvalue problem using\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper H Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">H<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf {H}^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -conforming finite elements. The key idea consists of \udb40\udc3cspan style=\udb40\udc22color:black\udb40\udc22\udb40\udc3econsidering a mixed method\udb40\udc3c\/span\udb40\udc3e controlling the divergence of the electric field in a fractional Sobolev space\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript negative alpha\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^{-\\alpha }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"alpha element-of left-parenthesis one half comma 1 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mfrac>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:mfrac>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\alpha \\in (\\frac 12,1)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The method is shown to be convergent and spectrally correct.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02464-6","type":"journal-article","created":{"date-parts":[[2011,2,4]],"date-time":"2011-02-04T13:33:04Z","timestamp":1296826384000},"page":"1887-1910","source":"Crossref","is-referenced-by-count":50,"title":["Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements"],"prefix":"10.1090","volume":"80","author":[{"given":"Andrea","family":"Bonito","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Luc","family":"Guermond","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,2,4]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1006\/jcph.1993.1214","article-title":"On a finite-element method for solving the three-dimensional Maxwell equations","volume":"109","author":"Assous, F.","year":"1993","journal-title":"J. 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