{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:11:32Z","timestamp":1776802292649,"version":"3.51.2"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"306","license":[{"start":{"date-parts":[[2017,10,7]],"date-time":"2017-10-07T00:00:00Z","timestamp":1507334400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171257"],"award-info":[{"award-number":["11171257"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We first establish anisotropic finite element estimates for the discrete Green\u2019s function of the Poisson equation. Then we prove that the bi-\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    rectangular finite element method under a specially designed partition has the highest possible convergent rate at all element vertices for the Poisson equation on the unit square. Furthermore, we provide numerical comparison with the standard uniform rectangular partition and demonstrate that our\n                    <italic>a priori<\/italic>\n                    superconvergent error estimate is sharp up to a logarithm factor.\n                  <\/p>","DOI":"10.1090\/mcom\/3159","type":"journal-article","created":{"date-parts":[[2016,5,11]],"date-time":"2016-05-11T09:43:58Z","timestamp":1462959838000},"page":"1693-1718","source":"Crossref","is-referenced-by-count":12,"title":["2\ud835\udc58 superconvergence of \ud835\udc44_{\ud835\udc58} finite elements by anisotropic mesh approximation in weighted Sobolev spaces"],"prefix":"10.1090","volume":"86","author":[{"given":"Wenming","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhimin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2016,10,7]]},"reference":[{"issue":"3-4","key":"1","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/BF02320197","article-title":"Anisotropic interpolation with applications to the finite element method","volume":"47","author":"Apel, T.","year":"1992","journal-title":"Computing","ISSN":"https:\/\/id.crossref.org\/issn\/0010-485X","issn-type":"print"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10092-004-0086-5","article-title":"The inf-sup condition for low order elements on anisotropic meshes","volume":"41","author":"Apel, T.","year":"2004","journal-title":"Calcolo","ISSN":"https:\/\/id.crossref.org\/issn\/0008-0624","issn-type":"print"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"843","DOI":"10.1093\/imanum\/21.4.843","article-title":"A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges","volume":"21","author":"Apel, Thomas","year":"2001","journal-title":"IMA J. 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