{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T18:09:36Z","timestamp":1780682976633,"version":"3.54.1"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"360","license":[{"start":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T00:00:00Z","timestamp":1781308800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1283\/2 2021 \u00e2?? 317210226"],"award-info":[{"award-number":["SFB 1283\/2 2021 \u00e2?? 317210226"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    For triangulations generated by the adaptive bisection algorithm by Maubach and Traxler we prove existence of a regularized mesh function with grading two. This sharpens previous results in two dimensions for the newest vertex bisection and generalizes them to arbitrary dimensions. In combination with Diening, Storn, and Tscherpel [SIAM J. Numer. Anal. 59 (2021), pp.\u00a02571\u20132607] this yields\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript 1\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -stability of the\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                    -projection onto Lagrange finite element spaces for all polynomial degrees and dimensions smaller than seven.\n                  <\/p>","DOI":"10.1090\/mcom\/4102","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T11:09:31Z","timestamp":1749812971000},"page":"1631-1678","source":"Crossref","is-referenced-by-count":1,"title":["Grading of triangulations generated by bisection"],"prefix":"10.1090","volume":"95","author":[{"given":"Lars","family":"Diening","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Storn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tabea","family":"Tscherpel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s00211-003-0492-7","article-title":"Adaptive finite element methods with convergence rates","volume":"97","author":"Binev, Peter","year":"2004","journal-title":"Numer. 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