{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T17:39:10Z","timestamp":1781890750037,"version":"3.54.5"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"264","license":[{"start":{"date-parts":[[2009,5,6]],"date-time":"2009-05-06T00:00:00Z","timestamp":1241568000000},"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 identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k greater-than-or-equal-to 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k\\ge 0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for both the potential as well as the flux, the order of convergence in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of both unknowns is\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Moreover, both the approximate potential as well as its numerical trace superconverge in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -like norms, to suitably chosen projections of the potential, with order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k plus 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k+2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k plus 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k+2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The method can be thought to be\n                    <italic>in between<\/italic>\n                    the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.\n                  <\/p>","DOI":"10.1090\/s0025-5718-08-02123-6","type":"journal-article","created":{"date-parts":[[2008,7,25]],"date-time":"2008-07-25T12:55:42Z","timestamp":1216990542000},"page":"1887-1916","source":"Crossref","is-referenced-by-count":234,"title":["A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems"],"prefix":"10.1090","volume":"77","author":[{"given":"Bernardo","family":"Cockburn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2008,5,6]]},"reference":[{"issue":"1","key":"1","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. 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