{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T18:19:24Z","timestamp":1783707564902,"version":"3.55.0"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"301","license":[{"start":{"date-parts":[[2016,11,10]],"date-time":"2016-11-10T00:00:00Z","timestamp":1478736000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1318108"],"award-info":[{"award-number":["1318108"]}],"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                    We define piecewise linear and continuous finite element methods for a class of interface problems in two dimensions. Correction terms are added to the right-hand side of the natural method to render it second-order accurate. We prove that the method is second-order accurate on general quasi-uniform meshes at the nodal points. Finally, we show that the natural method, although non-optimal near the interface, is optimal for points\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper O left-parenthesis StartRoot h log left-parenthesis StartFraction 1 Over h EndFraction right-parenthesis EndRoot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msqrt>\n                              <mml:mi>h<\/mml:mi>\n                              <mml:mi>log<\/mml:mi>\n                              <mml:mo>\n                                \u2061\n                                \n                              <\/mml:mo>\n                              <mml:mo stretchy=\"false\">(<\/mml:mo>\n                              <mml:mfrac>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mi>h<\/mml:mi>\n                              <\/mml:mfrac>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <\/mml:msqrt>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {O}(\\sqrt {h \\log (\\frac {1}{h})})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    away from the interface.\n                  <\/p>","DOI":"10.1090\/mcom3051","type":"journal-article","created":{"date-parts":[[2015,3,18]],"date-time":"2015-03-18T17:30:10Z","timestamp":1426699810000},"page":"2071-2098","source":"Crossref","is-referenced-by-count":28,"title":["On the accuracy of finite element approximations to a class of interface problems"],"prefix":"10.1090","volume":"85","author":[{"given":"Johnny","family":"Guzm\u00e1n","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manuel","family":"S\u00e1nchez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcus","family":"Sarkis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2015,11,10]]},"reference":[{"issue":"3","key":"1","first-page":"541","article-title":"Higher degree immersed finite element methods for second-order elliptic interface problems","volume":"11","author":"Adjerid, Slimane","year":"2014","journal-title":"Int. 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