{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T17:07:45Z","timestamp":1787591265570,"version":"build-2736575974"},"reference-count":64,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method is based on a parametric mapping which transforms a piecewise planar interface (or surface) reconstruction to a high order approximation. In the paper [C. Lehrenfeld and A. Reusken,<jats:italic>IMA J. Numer. Anal<\/jats:italic>.<jats:bold>38<\/jats:bold>(2018), No. 3, 1351\u20131387] an<jats:italic>a priori<\/jats:italic>error analysis of the method applied to an interface problem is presented. The analysis reveals optimal order discretization error bounds in the<jats:italic>H<\/jats:italic><jats:sup>1<\/jats:sup>-norm. In this paper we extend this analysis and derive optimal<jats:italic>L<\/jats:italic><jats:sup>2<\/jats:sup>-error bounds.<\/jats:p>","DOI":"10.1515\/jnma-2017-0109","type":"journal-article","created":{"date-parts":[[2018,1,31]],"date-time":"2018-01-31T10:01:54Z","timestamp":1517392914000},"page":"85-99","source":"Crossref","is-referenced-by-count":9,"title":["L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems"],"prefix":"10.1515","volume":"27","author":[{"given":"Christoph","family":"Lehrenfeld","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnold","family":"Reusken","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","reference":[{"key":"ref61","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1090\/S0025-5718-2010-02372-5","article-title":"A new multiscale finite element method for high-contrast elliptic interface problems","volume":"79","year":"2010","journal-title":"Math. 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