{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T04:13:44Z","timestamp":1783656824989,"version":"3.55.0"},"reference-count":43,"publisher":"American Mathematical Society (AMS)","issue":"330","license":[{"start":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T00:00:00Z","timestamp":1647388800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1717516"],"award-info":[{"award-number":["1717516"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor\u2013Hood (continuous\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper P 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf P_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    \u2013\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P 1\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>P<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">P_1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    ) bulk elements is proposed. A so-called volume normal derivative stabilization, known from the literature on trace FEM, is an essential ingredient of this method. The key result proved in the paper is an inf-sup stability of the trace\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold upper P 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">P<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbf P_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    \u2013\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P 1\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>P<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">P_1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh. Optimal order convergence of a consistent variant of the FEM follows from this new stability result and interpolation properties of the trace FEM. Properties of the method are illustrated with numerical examples.\n                  <\/p>","DOI":"10.1090\/mcom\/3551","type":"journal-article","created":{"date-parts":[[2020,4,1]],"date-time":"2020-04-01T09:43:42Z","timestamp":1585734222000},"page":"1527-1555","source":"Crossref","is-referenced-by-count":20,"title":["Inf-sup stability of the trace \ud835\udc0f\u2082\u2013\ud835\udc0f\u2081 Taylor\u2013Hood elements for surface PDEs"],"prefix":"10.1090","volume":"90","author":[{"given":"Maxim","family":"Olshanskii","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnold","family":"Reusken","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Zhiliakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2021,3,16]]},"reference":[{"key":"1","series-title":"Applied Mathematical Sciences","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/b97593","volume-title":"Topological methods in hydrodynamics","volume":"125","author":"Arnold, Vladimir I.","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/038794947X"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"031915","DOI":"10.1103\/PhysRevE.79.031915","article-title":"Relaxation dynamics of fluid membranes","volume":"79","author":"Arroyo, Marino","year":"2009","journal-title":"Phys. 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