{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:44:22Z","timestamp":1776843862654,"version":"3.51.2"},"reference-count":33,"publisher":"American Mathematical Society (AMS)","issue":"281","license":[{"start":{"date-parts":[[2013,4,13]],"date-time":"2013-04-13T00:00:00Z","timestamp":1365811200000},"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                    In this paper we consider the evolving surface finite element meth- od for the advection and diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a suitable variational formulation in time dependent Sobolev space we proposed and analysed a finite element method using surface finite elements on evolving triangulated surfaces. An optimal order\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                    -error bound was proved for linear finite elements. In this work we prove the optimal error bound in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared left-parenthesis normal upper Gamma left-parenthesis t right-parenthesis right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi>L<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u0393\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2(\\Gamma (t))<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    uniformly in time.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02601-9","type":"journal-article","created":{"date-parts":[[2012,4,13]],"date-time":"2012-04-13T09:15:00Z","timestamp":1334308500000},"page":"1-24","source":"Crossref","is-referenced-by-count":53,"title":["\ud835\udc3f\u00b2-estimates for the evolving surface finite element method"],"prefix":"10.1090","volume":"82","author":[{"given":"Gerhard","family":"Dziuk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Elliott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,4,13]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1016\/S0021-9991(02)00057-8","article-title":"Transport and diffusion of material quantities on propagating interfaces via level set methods","volume":"185","author":"Adalsteinsson, David","year":"2003","journal-title":"J. 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