{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:12:10Z","timestamp":1776845530311,"version":"3.51.2"},"reference-count":38,"publisher":"American Mathematical Society (AMS)","issue":"254","license":[{"start":{"date-parts":[[2006,12,16]],"date-time":"2006-12-16T00:00:00Z","timestamp":1166227200000},"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 devise and analyze a new local discontinuous Galerkin (LDG) method for the Stokes equations of incompressible fluid flow. This optimally convergent method is obtained by using an LDG method to discretize a vorticity-velocity formulation of the Stokes equations and by applying a new\n                    <italic>hybridization<\/italic>\n                    to the resulting discretization. One of the main features of the hybridized method is that it provides a globally divergence-free approximate velocity without having to construct globally divergence-free finite-dimensional spaces; only elementwise divergence-free basis functions are used. Another important feature is that it has significantly less degrees of freedom than all other LDG methods in the current literature; in particular, the approximation to the pressure is only defined on the faces of the elements. On the other hand, we show that, as expected, the condition number of the Schur-complement matrix for this approximate pressure is of order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h Superscript negative 2\">\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:mn>2<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">h^{-2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in the mesh size\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Finally, we present numerical experiments that confirm the sharpness of our theoretical a priori error estimates.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01804-1","type":"journal-article","created":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T11:05:20Z","timestamp":1140001520000},"page":"533-563","source":"Crossref","is-referenced-by-count":76,"title":["Hybridized globally divergence-free LDG methods. Part I: The Stokes problem"],"prefix":"10.1090","volume":"75","author":[{"given":"Jes\u00fas","family":"Carrero","sequence":"first","affiliation":[]},{"given":"Bernardo","family":"Cockburn","sequence":"additional","affiliation":[]},{"given":"Dominik","family":"Sch\u00f6tzau","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,12,16]]},"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. N.","year":"1985","journal-title":"RAIRO Mod\\'{e}l. Math. Anal. 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