{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T04:54:24Z","timestamp":1772340864451,"version":"3.50.1"},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100021856","name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["CUP E11G18000350001"],"award-info":[{"award-number":["CUP E11G18000350001"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider the non-symmetric coupling of finite and boundary elements to solve second-order nonlinear partial differential equations defined in unbounded domains.\nWe present a novel condition that ensures that the associated semi-linear form induces a strongly monotone operator, keeping track of the dependence on the linear combination of the interior domain equation with the boundary integral one.\nWe show that an optimal ellipticity condition, relating the nonlinear operator to the contraction constant of the shifted double-layer integral operator, is guaranteed by choosing a particular linear combination.\nThese results generalize those obtained by Of and Steinbach [Is the one-equation coupling of finite and boundary element methods always stable?, <jats:italic>ZAMM Z. Angew. Math. Mech.<\/jats:italic>\n                  <jats:bold>93<\/jats:bold> (2013), 6\u20137, 476\u2013484] and [On the ellipticity of coupled finite element and one-equation boundary element methods for boundary value problems, <jats:italic>Numer. Math.<\/jats:italic>\n                  <jats:bold>127<\/jats:bold> (2014), 3, 567\u2013593], and by Steinbach [A note on the stable one-equation coupling of finite and boundary elements, <jats:italic>SIAM J. Numer. Anal.<\/jats:italic>\n                  <jats:bold>49<\/jats:bold> (2011), 4, 1521\u20131531], where the simple sum of the two coupling equations has been considered.\nNumerical examples confirm the theoretical results on the sharpness of the presented estimates.<\/jats:p>","DOI":"10.1515\/cmam-2022-0085","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T13:36:11Z","timestamp":1678368971000},"page":"373-388","source":"Crossref","is-referenced-by-count":2,"title":["Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements"],"prefix":"10.1515","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2577-1421","authenticated-orcid":false,"given":"Matteo","family":"Ferrari","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Matematiche \u201cG.\u2009L. Lagrange\u201d , Politecnico di Torino , Corso Duca degli Abruzzi 24 , Turin , Italy"}]}],"member":"374","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"2023033113095810249_j_cmam-2022-0085_ref_001","doi-asserted-by":"crossref","unstructured":"M. Aurada, M. Feischl, T. F\u00fchrer, M. Karkulik, J. M. Melenk and D. Praetorius,\nClassical FEM-BEM coupling methods: Nonlinearities, well-posedness, and adaptivity,\nComput. Mech. 51 (2013), no. 4, 399\u2013419.","DOI":"10.1007\/s00466-012-0779-6"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_002","doi-asserted-by":"crossref","unstructured":"M. Aurada, M. Feischl and D. Praetorius,\nConvergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems,\nESAIM Math. Model. Numer. Anal. 46 (2012), no. 5, 1147\u20131173.","DOI":"10.1051\/m2an\/2011075"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_003","doi-asserted-by":"crossref","unstructured":"F. Brezzi and C. Johnson,\nOn the coupling of boundary integral and finite element methods,\nCalcolo 16 (1979), no. 2, 189\u2013201.","DOI":"10.1007\/BF02575926"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_004","doi-asserted-by":"crossref","unstructured":"M. Costabel,\nSymmetric methods for the coupling of finite elements and boundary elements (invited contribution),\nMathematical and Computational Aspects,\nSpringer, Berlin (1987), 411\u2013420.","DOI":"10.1007\/978-3-662-21908-9_26"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_005","doi-asserted-by":"crossref","unstructured":"M. Costabel,\nSome historical remarks on the positivity of boundary integral operators,\nBoundary Element Analysis,\nLect. Notes Appl. Comput. Mech. 29,\nSpringer, Berlin (2007), 1\u201327.","DOI":"10.1007\/978-3-540-47533-0_1"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_006","doi-asserted-by":"crossref","unstructured":"L. Desiderio, S. Falletta, M. Ferrari and L. Scuderi,\nCVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems,\nJ. Sci. Comput. 92 (2022), no. 3, Paper No. 96.","DOI":"10.1007\/s10915-022-01951-3"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_007","doi-asserted-by":"crossref","unstructured":"L. Desiderio, S. Falletta, M. Ferrari and L. Scuderi,\nOn the coupling of the curved virtual element method with the one-equation boundary element method for 2D exterior Helmholtz problems,\nSIAM J. Numer. Anal. 60 (2022), no. 4, 2099\u20132124.","DOI":"10.1137\/21M1460776"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_008","doi-asserted-by":"crossref","unstructured":"C. Erath, G. Of and F.-J. Sayas,\nA non-symmetric coupling of the finite volume method and the boundary element method,\nNumer. Math. 135 (2017), no. 3, 895\u2013922.","DOI":"10.1007\/s00211-016-0820-3"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_009","unstructured":"H. D. Han,\nA new class of variational formulations for the coupling of finite and boundary element methods,\nJ. Comput. Math. 8 (1990), no. 3, 223\u2013232."},{"key":"2023033113095810249_j_cmam-2022-0085_ref_010","doi-asserted-by":"crossref","unstructured":"G. C. Hsiao and W. L. Wendland,\nBoundary Integral Equations,\nAppl. Math. Sci. 164,\nSpringer, Berlin, 2008.","DOI":"10.1007\/978-3-540-68545-6"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_011","doi-asserted-by":"crossref","unstructured":"C. Johnson and J.-C. N\u00e9d\u00e9lec,\nOn the coupling of boundary integral and finite element methods,\nMath. Comp. 35 (1980), no. 152, 1063\u20131079.","DOI":"10.1090\/S0025-5718-1980-0583487-9"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_012","doi-asserted-by":"crossref","unstructured":"G. Of and O. Steinbach,\nIs the one-equation coupling of finite and boundary element methods always stable?,\nZAMM Z. Angew. Math. Mech. 93 (2013), no. 6\u20137, 476\u2013484.","DOI":"10.1002\/zamm.201100188"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_013","doi-asserted-by":"crossref","unstructured":"G. Of and O. Steinbach,\nOn the ellipticity of coupled finite element and one-equation boundary element methods for boundary value problems,\nNumer. Math. 127 (2014), no. 3, 567\u2013593.","DOI":"10.1007\/s00211-013-0593-x"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_014","doi-asserted-by":"crossref","unstructured":"G. J. Rodin and O. Steinbach,\nBoundary element preconditioners for problems defined on slender domains,\nSIAM J. Sci. Comput. 24 (2003), no. 4, 1450\u20131464.","DOI":"10.1137\/S1064827500372067"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_015","doi-asserted-by":"crossref","unstructured":"F.-J. Sayas,\nThe validity of Johnson-N\u00e9d\u00e9lec\u2019s BEM-FEM coupling on polygonal interfaces,\nSIAM J. Numer. Anal. 47 (2009), no. 5, 3451\u20133463.","DOI":"10.1137\/08072334X"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_016","doi-asserted-by":"crossref","unstructured":"O. Steinbach,\nNumerical Approximation Methods for Elliptic Boundary Value Problems,\nSpringer, New York, 2008.","DOI":"10.1007\/978-0-387-68805-3"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_017","doi-asserted-by":"crossref","unstructured":"O. Steinbach,\nA note on the stable one-equation coupling of finite and boundary elements,\nSIAM J. Numer. Anal. 49 (2011), no. 4, 1521\u20131531.","DOI":"10.1137\/090762701"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_018","doi-asserted-by":"crossref","unstructured":"O. Steinbach,\nOn the stability of the non-symmetric BEM\/FEM coupling in linear elasticity,\nComput. Mech. 51 (2013), no. 4, 421\u2013430.","DOI":"10.1007\/s00466-012-0782-y"},{"key":"2023033113095810249_j_cmam-2022-0085_ref_019","doi-asserted-by":"crossref","unstructured":"O. Steinbach and W. L. Wendland,\nOn C. Neumann\u2019s method for second-order elliptic systems in domains with non-smooth boundaries,\nJ. Math. Anal. Appl. 262 (2001), no. 2, 733\u2013748.","DOI":"10.1006\/jmaa.2001.7615"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0085\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0085\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T17:45:36Z","timestamp":1680284736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0085\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,10]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,10,6]]},"published-print":{"date-parts":[[2023,4,1]]}},"alternative-id":["10.1515\/cmam-2022-0085"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2022-0085","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,10]]}}}