{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:07:48Z","timestamp":1776802068142,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"303","license":[{"start":{"date-parts":[[2017,4,4]],"date-time":"2017-04-04T00:00:00Z","timestamp":1491264000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/J002313\/2"],"award-info":[{"award-number":["EP\/J002313\/2"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. The recently derived framework from previous works of the author is extended to include the case of a nonconforming approximation space. We show that the use of such a space allows us to reduce the amount of stabilization necessary for convergence, even in the case of ill-posed problems. We derive error estimates using conditional stability estimates in the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm.\n                  <\/p>","DOI":"10.1090\/mcom\/3092","type":"journal-article","created":{"date-parts":[[2015,8,6]],"date-time":"2015-08-06T08:53:18Z","timestamp":1438851198000},"page":"75-96","source":"Crossref","is-referenced-by-count":17,"title":["A stabilized nonconforming finite element method for the elliptic Cauchy problem"],"prefix":"10.1090","volume":"86","author":[{"given":"Erik","family":"Burman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2016,4,4]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00211-002-0436-7","article-title":"A priori and a posteriori analysis of finite volume discretizations of Darcy\u2019s equations","volume":"96","author":"Achdou, Y.","year":"2003","journal-title":"Numer. 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