{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T21:54:15Z","timestamp":1768686855548,"version":"3.49.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T00:00:00Z","timestamp":1571270400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T00:00:00Z","timestamp":1571270400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"crossref","award":["269\/17"],"award-info":[{"award-number":["269\/17"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s10915-019-01066-2","type":"journal-article","created":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T06:20:23Z","timestamp":1571293223000},"page":"1472-1492","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Complementary Solutions of Nitsche\u2019s Method"],"prefix":"10.1007","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9158-6603","authenticated-orcid":false,"given":"Isaac","family":"Harari","sequence":"first","affiliation":[]},{"given":"Uri","family":"Albocher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,10,17]]},"reference":[{"issue":"5","key":"1066_CR1","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1002\/nme.3339","volume":"90","author":"J Baiges","year":"2012","unstructured":"Baiges, J., Codina, R., Henke, F., Shahmiri, S., Wall, W.A.: A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int. J. Numer. Methods Eng. 90(5), 636\u2013658 (2012). \nhttps:\/\/doi.org\/10.1002\/nme.3339","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"1066_CR2","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1002\/nme.2755","volume":"82","author":"A Gerstenberger","year":"2010","unstructured":"Gerstenberger, A., Wall, W.A.: An embedded Dirichlet formulation for 3D continua. Int. J. Numer. Methods Eng. 82(5), 537\u2013563 (2010). \nhttps:\/\/doi.org\/10.1002\/nme.2755","journal-title":"Int. J. Numer. Methods Eng."},{"key":"1066_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717464","volume-title":"The Immersed Interface Method. Frontiers in Applied Mathematics","author":"Z Li","year":"2006","unstructured":"Li, Z., Ito, K.: The Immersed Interface Method. Frontiers in Applied Mathematics, vol. 33. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2006)"},{"issue":"47\u201348","key":"1066_CR4","doi-asserted-by":"publisher","first-page":"3358","DOI":"10.1016\/j.cma.2011.08.002","volume":"200","author":"D Schillinger","year":"2011","unstructured":"Schillinger, D., Rank, E.: An unfitted $$hp$$-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry. Comput. Methods Appl. Mech. Eng. 200(47\u201348), 3358\u20133380 (2011). \nhttps:\/\/doi.org\/10.1016\/j.cma.2011.08.002","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1066_CR5","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1016\/j.cma.2016.07.006","volume":"316","author":"F de Prenter","year":"2017","unstructured":"de Prenter, F., Verhoosel, C.V., van Zwieten, G.J., van Brummelen, E.H.: Condition number analysis and preconditioning of the finite cell method. Comput. Methods Appl. Mech. Eng. 316, 297\u2013327 (2017). \nhttps:\/\/doi.org\/10.1016\/j.cma.2016.07.006","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"1066_CR6","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF02995904","volume":"36","author":"J Nitsche","year":"1971","unstructured":"Nitsche, J.: Uber ein Variationsprinzip zur L\u00f6sung von Dirichlet\u2013Problemen bei Verwendung von Teilr\u00e4umen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hambg. 36(1), 9\u201315 (1971)","journal-title":"Abh. Math. Sem. Univ. Hambg."},{"issue":"1\u20133","key":"1066_CR7","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/0377-0427(95)00057-7","volume":"63","author":"R Stenberg","year":"1995","unstructured":"Stenberg, R.: On some techniques for approximating boundary conditions in the finite element method. J. Comput. Appl. Math. 63(1\u20133), 139\u2013148 (1995). \nhttps:\/\/doi.org\/10.1016\/0377-0427(95)00057-7","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"1066_CR8","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/0045-7825(91)90125-P","volume":"85","author":"HJB Barbosa","year":"1991","unstructured":"Barbosa, H.J.B., Hughes, T.J.R.: The finite element method with Lagrange multipliers on the boundary: circumventing the Babu\u0161ka\u2013Brezzi condition. Comput. Methods Appl. Mech. Eng. 85(1), 109\u2013128 (1991). \nhttps:\/\/doi.org\/10.1016\/0045-7825(91)90125-P","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1\u20132","key":"1066_CR9","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/S0045-7825(98)00051-6","volume":"164","author":"PE Barbone","year":"1998","unstructured":"Barbone, P.E., Montgomery, J.M., Ofer, O.M., Harari, I.: Scattering by a hybrid asymptotic\/finite element method. Comput. Methods Appl. Mech. Eng. 164(1\u20132), 141\u2013156 (1998). \nhttps:\/\/doi.org\/10.1016\/S0045-7825(98)00051-6","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"15","key":"1066_CR10","doi-asserted-by":"publisher","first-page":"2791","DOI":"10.1002\/(SICI)1097-0207(19970815)40:15<2791::AID-NME191>3.0.CO;2-W","volume":"40","author":"I Harari","year":"1997","unstructured":"Harari, I., Barbone, P.E., Montgomery, J.M.: Finite element formulations for exterior problems: application to hybrid methods, non-reflecting boundary conditions, and infinite elements. Int. J. Numer. Methods Eng. 40(15), 2791\u20132805 (1997). \nhttps:\/\/doi.org\/10.1002\/(SICI)1097-0207(19970815)40:15<2791::AID-NME191>3.0.CO;2-W","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"17","key":"1066_CR11","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.finel.2018.03.005","volume":"145","author":"I Harari","year":"2018","unstructured":"Harari, I., Albocher, U.: Spectral investigations of Nitsche\u2019s method. Finite Elem. Anal. Des. 145(17), 20\u201331 (2018). \nhttps:\/\/doi.org\/10.1016\/j.finel.2018.03.005","journal-title":"Finite Elem. Anal. Des."},{"issue":"2","key":"1066_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1002\/nme.2486","volume":"78","author":"J Dolbow","year":"2009","unstructured":"Dolbow, J., Harari, I.: An efficient finite element method for embedded interface problems. Internat. J. Numer. Methods Eng. 78(2), 229\u2013252 (2009). \nhttps:\/\/doi.org\/10.1002\/nme.2486\n\n. (Erratum: Ibid. 88(12):1344, (2011))","journal-title":"Internat. J. Numer. Methods Eng."},{"issue":"7","key":"1066_CR13","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1002\/nme.2863","volume":"83","author":"A Embar","year":"2010","unstructured":"Embar, A., Dolbow, J., Harari, I.: Imposing Dirichlet boundary conditions with Nitsche\u2019s method and spline-based finite elements. Int. J. Numer. Methods Eng. 83(7), 877\u2013898 (2010). \nhttps:\/\/doi.org\/10.1002\/nme.2863","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"47\u201348","key":"1066_CR14","doi-asserted-by":"publisher","first-page":"5537","DOI":"10.1016\/S0045-7825(02)00524-8","volume":"191","author":"A Hansbo","year":"2002","unstructured":"Hansbo, A., Hansbo, P.: An unfitted finite element method, based on Nitsche\u2019s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47\u201348), 5537\u20135552 (2002). \nhttps:\/\/doi.org\/10.1016\/S0045-7825(02)00524-8","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"1066_CR15","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1115\/1.2930242","volume":"114","author":"P Chen","year":"1992","unstructured":"Chen, P., Ginsberg, J.H.: On the relationship between veering of eigenvalue loci and parameter sensitivity of eigenfunctions. J. Vib. Acoust. 114(2), 141\u2013148 (1992). \nhttps:\/\/doi.org\/10.1115\/1.2930242","journal-title":"J. Vib. Acoust."},{"issue":"3","key":"1066_CR16","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0022-460X(86)90191-4","volume":"106","author":"NC Perkins","year":"1986","unstructured":"Perkins, N.C., Mote, C.D.: Comments on curve veering in eigenvalue problems. J. Sound Vib. 106(3), 451\u2013463 (1986). \nhttps:\/\/doi.org\/10.1016\/0022-460X(86)90191-4","journal-title":"J. Sound Vib."},{"key":"1066_CR17","volume-title":"Linear Algebra and Its Applications","author":"PD Lax","year":"2007","unstructured":"Lax, P.D.: Linear Algebra and Its Applications, 2nd edn. Wiley Interscience, Hoboken (2007)","edition":"2"},{"key":"1066_CR18","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.cma.2012.05.022","volume":"249\u2013252","author":"E Rank","year":"2012","unstructured":"Rank, E., Reuss, M., Kollmannsberger, S., Schillinger, D., D\u00fcster, A.: Geometric modeling, isogeometric analysis and the finite cell method. Comput. Methods Appl. Mech. Eng. 249\u2013252, 104\u2013115 (2012). \nhttps:\/\/doi.org\/10.1016\/j.cma.2012.05.022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1066_CR19","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1017\/S0001924000062618","volume":"67","author":"BM Irons","year":"1963","unstructured":"Irons, B.M.: Eigenvalue economisers in vibration problems. J. R. Aeronaut. Soc. 67, 526\u2013528 (1963). \nhttps:\/\/doi.org\/10.1017\/S0001924000062618","journal-title":"J. R. Aeronaut. Soc."},{"key":"1066_CR20","doi-asserted-by":"publisher","first-page":"380","DOI":"10.2514\/3.2874","volume":"3","author":"R Guyan","year":"1965","unstructured":"Guyan, R.: Reduction of stiffness and mass matrices. AIAA J. 3, 380\u2013387 (1965). \nhttps:\/\/doi.org\/10.2514\/3.2874","journal-title":"AIAA J."},{"issue":"4","key":"1066_CR21","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/j.apnum.2011.01.008","volume":"62","author":"E Burman","year":"2012","unstructured":"Burman, E., Hansbo, P.: Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62(4), 328\u2013341 (2012). \nhttps:\/\/doi.org\/10.1016\/j.apnum.2011.01.008","journal-title":"Appl. Numer. Math."},{"issue":"7","key":"1066_CR22","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1002\/nme.4823","volume":"104","author":"E Burman","year":"2015","unstructured":"Burman, E., Claus, S., Hansbo, P., Larson, M., Massing, A.: CutFEM: discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104(7), 472\u2013501 (2015). \nhttps:\/\/doi.org\/10.1002\/nme.4823","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"1066_CR23","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1002\/nme.2312","volume":"76","author":"AJ Lew","year":"2008","unstructured":"Lew, A.J., Buscaglia, G.C.: A discontinuous-Galerkin-based immersed boundary method. Int. J. Numer. Methods Eng. 76(4), 427\u2013454 (2008). \nhttps:\/\/doi.org\/10.1002\/nme.2312","journal-title":"Int. J. Numer. Methods Eng."},{"key":"1066_CR24","volume-title":"An Analysis of the Finite Element Method","author":"G Strang","year":"1973","unstructured":"Strang, G., Fix, G.: An Analysis of the Finite Element Method. Prentice-Hall Inc, Englewood Cliffs (1973)"},{"key":"1066_CR25","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1016\/j.cma.2013.11.012","volume":"272","author":"TJR Hughes","year":"2014","unstructured":"Hughes, T.J.R., Evans, J.A., Reali, A.: Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems. Comput. Methods Appl. Mech. Eng. 272, 290\u2013320 (2014). \nhttps:\/\/doi.org\/10.1016\/j.cma.2013.11.012","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"12","key":"1066_CR26","doi-asserted-by":"publisher","first-page":"4322","DOI":"10.1016\/j.camwa.2018.03.032","volume":"75","author":"F de Prenter","year":"2018","unstructured":"de Prenter, F., Lehrenfeld, C., Massing, A.: A note on the stability parameter in Nitsche\u2019s method for unfitted boundary value problems. Comput. Math. Appl. 75(12), 4322\u20134336 (2018). \nhttps:\/\/doi.org\/10.1016\/j.camwa.2018.03.032","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"1066_CR27","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1002\/nme.4343","volume":"92","author":"C Annavarapu","year":"2012","unstructured":"Annavarapu, C., Hautefeuille, M., Dolbow, J.E.: Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int. J. Numer. Methods Eng. 92(2), 206\u2013228 (2012). \nhttps:\/\/doi.org\/10.1002\/nme.4343","journal-title":"Int. J. Numer. Methods Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-01066-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-019-01066-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-01066-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T23:15:42Z","timestamp":1602803742000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-019-01066-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,17]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["1066"],"URL":"https:\/\/doi.org\/10.1007\/s10915-019-01066-2","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,17]]},"assertion":[{"value":"13 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}