{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:24:23Z","timestamp":1787329463222,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005714","name":"Technische Universit\u00e4t Darmstadt","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005714","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We consider the numerical approximation of parabolic-elliptic interface problems by the nonsymmetric coupling method of MacCamy and Suri [ Quart. Appl. Math., 44 (1987), pp. 675--690]. We establish well-posedness of this formulation for problems with nonsmooth interfaces and prove quasioptimality for a class of conforming Galerkin approximations in space. Therefore, error estimates with optimal order can be deduced for the semidiscretization in space by appropriate finite and boundary elements. Moreover, we investigate the subsequent discretization in time by a variant of the implicit Euler method. As for the semidiscretization, we establish well-posedness and quasi optimality for the fully discrete scheme under minimal regularity assumptions on the solution. Error estimates with optimal order follow again directly. Our analysis is based on estimates in appropriate energy norms. Thus, we do not use duality arguments and corresponding estimates for an elliptic projection which are not available for the nonsymmetric coupling method. Additionally, we provide again error estimates under minimal regularity assumptions. Some numerical examples illustrate our theoretical results.<\/jats:p>","DOI":"10.1137\/17m1158276","type":"journal-article","created":{"date-parts":[[2018,12,11]],"date-time":"2018-12-11T14:09:26Z","timestamp":1544537366000},"page":"3510-3533","source":"Crossref","is-referenced-by-count":4,"title":["On the Nonsymmetric Coupling Method for Parabolic-Elliptic Interface Problems"],"prefix":"10.1137","volume":"56","author":[{"given":"Herbert","family":"Egger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Erath","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0811-5473","authenticated-orcid":true,"given":"Robert","family":"Schorr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,12,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-013-9771-2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-012-0779-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-01-01314-X"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-013-0562-4"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/1052136"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1115\/1.3424474"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/0519043"},{"key":"atypb9","first-page":"281","volume-title":"The Mathematics of Finite Elements and Applications","author":"Costabel M.","year":"1987"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/1995290707791"},{"key":"atypb11","volume-title":"Mathematical Analysis and Numerical Methods for Science and Technology","volume":"5","author":"Dautray R.","year":"1992"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-016-0820-3"},{"key":"atypb13","volume-title":"University of Ulm","author":"Erath C.","year":"2010"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-96415-7_94"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/019"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drv044"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2006.03.018"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1980-0583487-9"},{"key":"atypb19","volume-title":"Strongly Elliptic Systems and Boundary Integral Equations","author":"McLean W.","year":"2000"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/872820"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/08072334X"},{"key":"atypb22","volume-title":"Texts Appl. Math.","author":"Steinbach O.","year":"2008"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/090762701"},{"key":"atypb24","unstructured":"F. Tantardini,\n                      Quasi-Optimality in the Backward Euler-Galerkin Method for Linear Parabolic Problems\n                      , Ph.D. thesis, Universit\u00e0 degli Studi di Milano, Milan, Italy, 2014."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970647"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/0710062"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1158276","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:18:22Z","timestamp":1787325502000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1158276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":26,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1158276"],"URL":"https:\/\/doi.org\/10.1137\/17m1158276","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}