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Comp."],"abstract":"<p>\n                    We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"u element-of upper H Superscript s\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>u<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>H<\/mml:mi>\n                              <mml:mi>s<\/mml:mi>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">u \\in H^s<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s element-of left-parenthesis 1 comma 3 slash 2 right-bracket\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo stretchy=\"false\">]<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">s\\in (1,3\/2]<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.\n                  <\/p>","DOI":"10.1090\/mcom\/3875","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T09:33:35Z","timestamp":1686735215000},"page":"35-54","source":"Crossref","is-referenced-by-count":0,"title":["Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions"],"prefix":"10.1090","volume":"93","author":[{"given":"Erik","family":"Burman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Hansbo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mats","family":"Larson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"issue":"7","key":"1","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1002\/nme.4823","article-title":"CutFEM: discretizing geometry and partial differential equations","volume":"104","author":"Burman, Erik","year":"2015","journal-title":"Internat. 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