{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T14:37:22Z","timestamp":1791383842449,"version":"4.3.3"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non\u2013body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the discontinuities across the interface in the solution and flux are removed, and an equivalent elliptic interface problem with homogeneous jump conditions is formulated. Special finite-element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions. Error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate. These methods are designed as an efficient component of the finite-element level-set methodology for fast simulation of interface dynamics that does not require remeshing.<\/jats:p>","DOI":"10.1137\/060666482","type":"journal-article","created":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T18:05:46Z","timestamp":1201716346000},"page":"472-495","source":"Crossref","is-referenced-by-count":213,"title":["Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions"],"prefix":"10.1137","volume":"46","author":[{"given":"Yan","family":"Gong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhilin","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,1,30]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501389849"},{"key":"R2","unstructured":"R. Adams,\n                      Sobolev Spaces\n                      , Academic Press, New York, 1975."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.029"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"S. C. Brenner and L. R. Scott,\n                      The Mathematical Theory of Finite Element Methods\n                      , 2nd ed., Springer-Verlag, New York, 2002.","DOI":"10.1007\/978-1-4757-3658-8"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1951.0006"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S1540345902407208"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050336"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"P. G. 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Johnson,\n                      Numerical Solution of Partial Differential Equations by the Finite Element Method\n                      , Cambridge University Press, Cambridge, UK, 1987."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995291329"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500370160"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Z. Li and K. Ito,\n                      The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains\n                      , Frontiers Appl. Math. 33, SIAM, Philadelphia, 2006.","DOI":"10.1137\/1.9780898717464"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-003-0473-x"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750139618X"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"S. Osher and R. 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Schultz et al., eds., Academic Press, New York, 1981, pp. 163\u2013185.","DOI":"10.1016\/B978-0-12-632620-8.50013-9"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060666482","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:10:21Z","timestamp":1787325021000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060666482"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060666482"],"URL":"https:\/\/doi.org\/10.1137\/060666482","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}