{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T14:02:36Z","timestamp":1776866556312,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"280","license":[{"start":{"date-parts":[[2013,3,1]],"date-time":"2013-03-01T00:00:00Z","timestamp":1362096000000},"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                    The aim of the paper is to show the stability of the finite element solution for the Stokes system in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper W Subscript normal infinity Superscript 1\">\n                        <mml:semantics>\n                          <mml:msubsup>\n                            <mml:mi>W<\/mml:mi>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msubsup>\n                          <mml:annotation encoding=\"application\/x-tex\">W^1_\\infty<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    norm on general convex polyhedral domain. In contrast to previously known results,\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper W Subscript r Superscript 2\">\n                        <mml:semantics>\n                          <mml:msubsup>\n                            <mml:mi>W<\/mml:mi>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msubsup>\n                          <mml:annotation encoding=\"application\/x-tex\">W^2_r<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    regularity for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"r greater-than 3\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>r<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">r&gt;3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , which does not hold for general convex polyhedral domains, is not required. The argument uses recently available sharp H\u00f6lder pointwise estimates of the corresponding Green\u2019s matrix together with novel local energy error estimates, which do not involve an error of the pressure in a weaker norm.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02603-2","type":"journal-article","created":{"date-parts":[[2012,3,1]],"date-time":"2012-03-01T16:40:51Z","timestamp":1330620051000},"page":"1879-1902","source":"Crossref","is-referenced-by-count":21,"title":["Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra"],"prefix":"10.1090","volume":"81","author":[{"given":"J.","family":"Guzm\u00e1n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Leykekhman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,3,1]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1051\/m2an\/1995290303671","article-title":"Local error estimates for finite element discretizations of the Stokes equations","volume":"29","author":"Arnold, Douglas N.","year":"1995","journal-title":"RAIRO Mod\\'{e}l. 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