{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T04:06:21Z","timestamp":1773201981226,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"name":"DFG Research Center Matheon"},{"DOI":"10.13039\/100016838","name":"Berlin Mathematical School","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100016838","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,7,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>With newest vertex bisection, there is no uniform bound on the number of <jats:italic>n<\/jats:italic>-simplices that need to be refined to arrive at the smallest conforming refinement <jats:inline-formula id=\"eq1_w2aab2b8c25b1b7b1aab1c13b1b3Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2014-0013_566968c00602e5e291b78478a1df8ac8.png\"\/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>\ud835\udcaf<\/m:mi>\n                              <m:mo>'<\/m:mo>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:tex-math>$\\mathcal {T}^{\\prime }$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of a conforming partition <jats:inline-formula id=\"eq2_w2aab2b8c25b1b7b1aab1c13b1b5Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2014-0013_6f03fe8cea2ac320365ddd86bd7cc506.png\"\/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mi>\ud835\udcaf<\/m:mi>\n                        <\/m:math>\n                        <jats:tex-math>$\\mathcal {T}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> in which one simplex has been bisected. In this note, we show that the difference in levels between any <jats:inline-formula id=\"eq3_w2aab2b8c25b1b7b1aab1c13b1b7Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2014-0013_1f49489a669a131f796b77c7190b2175.png\"\/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msup>\n                                 <m:mi>T<\/m:mi>\n                                 <m:mo>'<\/m:mo>\n                              <\/m:msup>\n                              <m:mo>\u2208<\/m:mo>\n                              <m:msup>\n                                 <m:mi>\ud835\udcaf<\/m:mi>\n                                 <m:mo>'<\/m:mo>\n                              <\/m:msup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>$T^{\\prime } \\in \\mathcal {T}^{\\prime }$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and its ancestor <jats:inline-formula id=\"eq4_w2aab2b8c25b1b7b1aab1c13b1b9Aa\">\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cmam-2014-0013_ac26099fa78b427c1023bfeea40822d3.png\"\/>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>T<\/m:mi>\n                              <m:mo>\u2208<\/m:mo>\n                              <m:mi>\ud835\udcaf<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:tex-math>$T \\in \\mathcal {T}$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>\n                  <jats:italic>is<\/jats:italic> uniformly bounded.\nThis result has been used in\nLemma 4.2 of [SIAM J. Numer. Anal. 51 (2013), 2935\u20132955]\nby Carstensen and the first two authors.<\/jats:p>","DOI":"10.1515\/cmam-2014-0013","type":"journal-article","created":{"date-parts":[[2014,5,21]],"date-time":"2014-05-21T12:51:20Z","timestamp":1400676680000},"page":"317-320","source":"Crossref","is-referenced-by-count":17,"title":["A Remark on Newest Vertex Bisection in Any Space Dimension"],"prefix":"10.1515","volume":"14","author":[{"given":"Dietmar","family":"Gallistl","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mira","family":"Schedensack","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Unter den Linden 6, 10099 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rob P.","family":"Stevenson","sequence":"additional","affiliation":[{"name":"Korteweg\u2013de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,5,1]]},"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/14\/3\/article-p317.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0013\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0013\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T21:08:34Z","timestamp":1680296914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2014-0013\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,4,24]]},"published-print":{"date-parts":[[2014,7,1]]}},"alternative-id":["10.1515\/cmam-2014-0013"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2014-0013","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,1]]}}}