{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:29:33Z","timestamp":1787329773132,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We consider an unsteady convection diffusion equation which models the transport of a dissolved species in two-phase incompressible flow problems. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. In [A. Hansbo and P. Hansbo, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp. 5537--5552], for the purely elliptic stationary case, an extended finite element method (XFEM) is combined with a Nitsche-type method, and optimal error bounds are derived. These results were extended to the unsteady case in [A. Reusken and T. Nguyen, J. Fourier Anal. Appl., 15 (2009), pp. 663--683]. In the latter paper convection terms are also considered but assumed to be small. In many two-phase flow applications, however, convection is the dominant transport mechanism. Hence there is a need for a stable numerical method for the case of a convection dominated transport equation. In this paper we address this topic and study the streamline diffusion stabilization for the Nitsche-XFEM. The method is presented, and results of numerical experiments are given that indicate that this kind of stabilization is satisfactory for this problem class. Furthermore, a theoretical error analysis of the stabilized Nitsche-XFEM is presented that results in optimal a priori discretization error bounds.<\/jats:p>","DOI":"10.1137\/110855235","type":"journal-article","created":{"date-parts":[[2012,10,11]],"date-time":"2012-10-11T13:45:02Z","timestamp":1349963102000},"page":"A2740-A2759","source":"Crossref","is-referenced-by-count":18,"title":["Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem"],"prefix":"10.1137","volume":"34","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":"351","published-online":{"date-parts":[[2012,10,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2009.06.017"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/nme.3093"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18540-3_13"},{"key":"atypb5","volume-title":"Proceedings of the 2003 ASME Joint U.S.-European Fluids Engineering Conference","author":"Bothe D.","year":"2003"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202511005659"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/050634736"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15337-2_12"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1115\/1.1526599"},{"key":"atypb10","volume-title":"Finite Elements and Fast Iterative Solvers","author":"Elman H.","year":"2005"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-006-0024-y"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-19686-7"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00524-8"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2003.12.041"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2003039"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0587-4"},{"key":"atypb17","volume-title":"Eyrolles","author":"Ishii M.","year":"1975"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.10.003"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-008-0099-8"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-009-9092-y"},{"key":"atypb21","volume-title":"Numerical Methods for Singularly Perturbed Differential Equations---Convection-Diffusion and Flow Problems","author":"Roos H.-G.","year":"2008","edition":"2"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4022-8"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511800238"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050056"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2003018"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/110855235","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:33:03Z","timestamp":1787326383000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/110855235"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":25,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/110855235"],"URL":"https:\/\/doi.org\/10.1137\/110855235","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}