{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T19:25:16Z","timestamp":1780687516391,"version":"3.54.1"},"reference-count":39,"publisher":"American Mathematical Society (AMS)","issue":"278","license":[{"start":{"date-parts":[[2012,9,29]],"date-time":"2012-09-29T00:00:00Z","timestamp":1348876800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We consider finite element methods for a model second-order elliptic equation on a general bounded convex polygonal or polyhedral domain. Our first main goal is to extend the best approximation property of the error in the\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:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"normal\">\n                                \u221e\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\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, which is known to hold on quasi-uniform meshes, to more general graded meshes. We accomplish it by a novel proof technique. This result holds under a condition on the grid which is mildly more restrictive than the shape regularity condition typically enforced in adaptive codes. The second main contribution of this work is a discussion of the properties of and relationships between similar mesh restrictions that have appeared in the literature.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02546-9","type":"journal-article","created":{"date-parts":[[2011,9,29]],"date-time":"2011-09-29T15:12:05Z","timestamp":1317309125000},"page":"743-764","source":"Crossref","is-referenced-by-count":38,"title":["Best approximation property in the \ud835\udc4a\u00b9_{\u221e} norm for finite element methods on graded meshes"],"prefix":"10.1090","volume":"81","author":[{"given":"A.","family":"Demlow","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Leykekhman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Schatz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Wahlbin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,9,29]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"1771","DOI":"10.1137\/080731724","article-title":"\ud835\udc3f^{\u221e}-error estimates on graded meshes with application to optimal control","volume":"48","author":"Apel, Thomas","year":"2009","journal-title":"SIAM J. 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