{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:38:26Z","timestamp":1787330306781,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In a recent paper [C. Lehrenfeld and A. Reusken, SIAM J. Numer. Anal., 51 (2013), pp. 958--983] a new finite element discretization method for a class of two-phase mass transport problems is presented and analyzed. The transport problem describes mass transport in a domain with an evolving interface. Across the evolving interface a jump condition has to be satisfied. The discretization in that paper is a space-time approach which combines a discontinuous Galerkin (DG) technique (in time) with an extended finite element method (XFEM). Using the Nitsche method the jump condition is enforced in a weak sense. While the emphasis in that paper was on the analysis and one-dimensional numerical experiments the main contribution of this paper is the discussion of implementation aspects for the spatially three-dimensional case. As the space-time interface is typically given only implicitly as the zero-level of a level-set function, we construct a piecewise planar approximation of the space-time interface. This discrete interface is used to divide the space-time domain into its subdomains. An important component within this decomposition is a new method for dividing four-dimensional prisms intersected by a piecewise planar space-time interface into simplices. Such a subdivision algorithm is necessary for numerical integration on the subdomains as well as on the space-time interface. These numerical integrations are needed in the implementation of the Nitsche XFEM-DG method in three space dimensions. Corresponding numerical studies are presented and discussed.<\/jats:p>","DOI":"10.1137\/130943534","type":"journal-article","created":{"date-parts":[[2015,1,29]],"date-time":"2015-01-29T09:11:06Z","timestamp":1422522666000},"page":"A245-A270","source":"Crossref","is-referenced-by-count":39,"title":["The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions"],"prefix":"10.1137","volume":"37","author":[{"given":"Christoph","family":"Lehrenfeld","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,29]]},"reference":[{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2009.06.017"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1796"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18540-3_13"},{"key":"atypb5","first-page":"423","volume-title":"Proceedings of the 4th ASME\/JSME Joint Fluids Engineering Conference, Honolulu, 2003","author":"Bothe D.","year":"2003"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2011.01.008"},{"key":"atypb7","first-page":"227","volume-title":"Frontiers in Numerical Analysis - Durham","author":"Burman E.","year":"2010"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15337-2_12"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1155"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/0719090"},{"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":"Master's thesis","author":"Holasch S.","year":"1991"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/110855235"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/120875260"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4569"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.10.003"},{"key":"atypb22","unstructured":"M. Neum\u00fcller,\n                      Space-Time Methods, Fast Solvers and Applications\n                      , Ph.D. Thesis, TU Graz, Graz, Austria, 2013."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-012-0174-z"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-009-9092-y"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4022-8"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511800238"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.2307\/2005635"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03359-3"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.02.010"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130943534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:56:48Z","timestamp":1787327808000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130943534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130943534"],"URL":"https:\/\/doi.org\/10.1137\/130943534","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}