{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T17:17:57Z","timestamp":1781284677871,"version":"3.54.1"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"257","license":[{"start":{"date-parts":[[2007,8,7]],"date-time":"2007-08-07T00:00:00Z","timestamp":1186444800000},"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                    In this paper, we uncover and study a new superconvergence property of a large class of finite element methods for one-dimensional convection-diffusion problems. This class includes discontinuous Galerkin methods defined in terms of numerical traces, discontinuous Petrov\u2013Galerkin methods and hybridized mixed methods. We prove that the so-called numerical traces of\n                    <italic>both<\/italic>\n                    variables superconverge at\n                    <italic>all<\/italic>\n                    the nodes of the mesh, provided that the traces are\n                    <italic>conservative<\/italic>\n                    , that is, provided they are single-valued. In particular, for a local discontinuous Galerkin method, we show that the superconvergence is order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2 p plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">2\\,p+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    when polynomials of degree at most\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are used. Extensive numerical results verifying our theoretical results are displayed.\n                  <\/p>","DOI":"10.1090\/s0025-5718-06-01895-3","type":"journal-article","created":{"date-parts":[[2006,11,1]],"date-time":"2006-11-01T16:50:02Z","timestamp":1162399802000},"page":"67-96","source":"Crossref","is-referenced-by-count":88,"title":["Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension"],"prefix":"10.1090","volume":"76","author":[{"given":"Fatih","family":"Celiker","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernardo","family":"Cockburn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2006,8,7]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10915-004-4133-9","article-title":"Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems","volume":"22\/23","author":"Adjerid, Slimane","year":"2005","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1137\/0719052","article-title":"An interior penalty finite element method with discontinuous elements","volume":"19","author":"Arnold, Douglas N.","year":"1982","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1051\/m2an\/1985190100071","article-title":"Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates","volume":"19","author":"Arnold, D. N.","year":"1985","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. 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