{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T01:07:35Z","timestamp":1780621655691,"version":"3.54.1"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T00:00:00Z","timestamp":1713744000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T00:00:00Z","timestamp":1713744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100010583","name":"Universit\u00e4t Konstanz","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010583","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":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider a time-stepping scheme of Crank\u2013Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step is required. Following Lehrenfeld and Olskanskii (ESAIM: M2AN 53(2):585\u2013614, 2019), we apply an implicit extension based on so-called ghost-penalty terms. For spatial discretisation, a cut finite element method is used. We derive a complete a priori error analysis in space and time, which shows in particular second-order convergence in time under a parabolic CFL condition. Finally, we present numerical results in two and three space dimensions that confirm the analytical estimates, even for much larger time steps.<\/jats:p>","DOI":"10.1007\/s10915-024-02530-4","type":"journal-article","created":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T08:01:58Z","timestamp":1713772918000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Implicitly Extended Crank\u2013Nicolson Scheme for the Heat Equation on a Time-Dependent Domain"],"prefix":"10.1007","volume":"99","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4507-4690","authenticated-orcid":false,"given":"Stefan","family":"Frei","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maneesh Kumar","family":"Singh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,22]]},"reference":[{"key":"2530_CR1","unstructured":"Aln\u00e6s, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Arch. Numer. Soft. 3(100) (2015). https:\/\/doi.org\/10.11588\/ans.2015.100.20553"},{"key":"2530_CR2","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1142\/S0219876204000083","volume":"1","author":"I Babu\u0161ka","year":"2004","unstructured":"Babu\u0161ka, I., Banarjee, U., Osborn, J.E.: Generalized finite element methods: main ideas, results, and perspective. Int. J. Comput. Methods 1, 67\u2013103 (2004)","journal-title":"Int. J. Comput. Methods"},{"key":"2530_CR3","doi-asserted-by":"crossref","DOI":"10.1002\/9781118483565","volume-title":"Computational Fluid\u2013Structure Interaction: Methods and Applications","author":"Y Bazilevs","year":"2013","unstructured":"Bazilevs, Y., Takizawa, K., Tezduyar, T.E.: Computational Fluid\u2013Structure Interaction: Methods and Applications. Wiley, Hoboken (2013)"},{"key":"2530_CR4","unstructured":"Becker, R.: An adaptive finite element method for the incompressible Navier\u2013Stokes equations on time-dependent domains. Ph.D. thesis, Habilitation Thesis, University of Heidelberg, Germany (1995)"},{"key":"2530_CR5","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF02127700","volume":"6","author":"JH Bramble","year":"1996","unstructured":"Bramble, J.H., King, J.T.: A finite element method for interface problems in domains with smooth boundaries and interfaces. Adv. Comput. Math. 6, 109\u2013138 (1996)","journal-title":"Adv. Comput. Math."},{"key":"2530_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The Mathematical Theory of Finite Element Methods","author":"SC Brenner","year":"2008","unstructured":"Brenner, S.C.: The Mathematical Theory of Finite Element Methods. Springer, Berlin (2008)"},{"issue":"21\u201322","key":"2530_CR7","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1016\/j.crma.2010.10.006","volume":"348","author":"E Burman","year":"2010","unstructured":"Burman, E.: Ghost penalty. C. R. Math. 348(21\u201322), 1217\u20131220 (2010)","journal-title":"C. R. Math."},{"issue":"7","key":"2530_CR8","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1002\/nme.4823","volume":"104","author":"E Burman","year":"2015","unstructured":"Burman, E., Claus, S., Hansbo, P., Larson, M.G., Massing, A.: Cutfem: discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104(7), 472\u2013501 (2015)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"2","key":"2530_CR9","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1051\/m2an\/2019072","volume":"54","author":"E Burman","year":"2020","unstructured":"Burman, E., Fern\u00e1ndez, M.A., Frei, S.: A Nitsche-based formulation for fluid\u2013structure interactions with contact. ESAIM: M2AN 54(2), 531\u2013564 (2020)","journal-title":"ESAIM: M2AN"},{"key":"2530_CR10","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114637","volume":"392","author":"E Burman","year":"2022","unstructured":"Burman, E., Fern\u00e1ndez, M.A., Frei, S., Gerosa, F.M.: A mechanically consistent model for fluid\u2013structure interactions with contact including seepage. Comput. Methods Appl. Mech. Eng. 392, 114637 (2022)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR11","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.cma.2014.07.007","volume":"279","author":"E Burman","year":"2014","unstructured":"Burman, E., Fern\u00e1ndez, M.A.: An unfitted Nitsche method for incompressible fluid\u2013structure interaction using overlapping meshes. Comput. Methods Appl. Mech. Eng. 279, 497\u2013514 (2014)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR12","doi-asserted-by":"crossref","unstructured":"Burman, E., Frei, S., Massing, A.: Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains. Numer. Math. 150, 423\u2013478 (2022)","DOI":"10.1007\/s00211-021-01264-x"},{"issue":"310","key":"2530_CR13","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1090\/mcom\/3240","volume":"87","author":"E Burman","year":"2018","unstructured":"Burman, E., Hansbo, P., Larson, M.G.: A cut finite element method with boundary value correction. Math. Comput. 87(310), 633\u2013657 (2018)","journal-title":"Math. Comput."},{"issue":"2","key":"2530_CR14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/s00211-015-0744-3","volume":"133","author":"E Burman","year":"2016","unstructured":"Burman, E., Hansbo, P., Larson, M.G., Zahedi, S.: Cut finite element methods for coupled bulk-surface problems. Numer. Math. 133(2), 203\u2013231 (2016)","journal-title":"Numer. Math."},{"issue":"5","key":"2530_CR15","doi-asserted-by":"crossref","first-page":"6410","DOI":"10.1007\/s40314-018-0692-5","volume":"37","author":"LJ Caucha","year":"2018","unstructured":"Caucha, L.J., Frei, S., Rubio, O.: Finite element simulation of fluid dynamics and $$\\text{ CO}_2$$ gas exchange in the alveolar sacs of the human lung. Comput. Appl. Math. 37(5), 6410\u20136432 (2018)","journal-title":"Comput. Appl. Math."},{"issue":"1","key":"2530_CR16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1115\/1.1526599","volume":"70","author":"J Chessa","year":"2003","unstructured":"Chessa, J., Belytschko, T.: An extended finite element method for two-phase fluids. J. Appl. Mech. 70(1), 10\u201317 (2003)","journal-title":"J. Appl. Mech."},{"key":"2530_CR17","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.cma.2019.01.009","volume":"348","author":"S Claus","year":"2019","unstructured":"Claus, S., Kerfriden, P.: A CutFEM method for two-phase flow problems. Comput. Methods Appl. Mech. Eng. 348, 185\u2013206 (2019)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"2530_CR18","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1016\/j.jcp.2008.11.004","volume":"228","author":"R Codina","year":"2009","unstructured":"Codina, R., Houzeaux, G., Coppola-Owen, H., Baiges, J.: The fixed-mesh ALE approach for the numerical approximation of flows in moving domains. J. Comput. Phys. 228(5), 1591\u20131611 (2009)","journal-title":"J. Comput. Phys."},{"key":"2530_CR19","volume-title":"Multiphase Flows with Droplets and Particles","author":"CT Crowe","year":"1997","unstructured":"Crowe, C.T., Schwarzkopf, J.D., Sommerfeld, M., Tsuji, Y.: Multiphase Flows with Droplets and Particles. Taylor & Francis, Oxford (1997)"},{"issue":"12","key":"2530_CR20","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1002\/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L","volume":"48","author":"C Daux","year":"2000","unstructured":"Daux, C., Mo\u00ebs, N., Dolbow, J., Sukumar, N., Belytschko, T.: Arbitrary branched and intersecting cracks with the extended finite element method. Int. J. Numer. Methods Eng. 48(12), 1741\u20131760 (2000)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"1\u20133","key":"2530_CR21","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/0045-7825(82)90128-1","volume":"33","author":"J Donea","year":"1982","unstructured":"Donea, J., Giuliani, S., Halleux, J.-P.: An arbitrary Lagrangian\u2013Eulerian finite element method for transient dynamic fluid\u2013structure interactions. Comput. Methods Appl. Mech. Eng. 33(1\u20133), 689\u2013723 (1982)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR22","unstructured":"Donea, J., Huerta, A., Ponthot, J.-P., Rodr\u00edguez-Ferran, A.: Arbitrary Lagrangian\u2013Eulerian Methods. Wiley Online Library (2004)"},{"issue":"9\u201310","key":"2530_CR23","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1002\/fld.1205","volume":"51","author":"T Dunne","year":"2006","unstructured":"Dunne, T.: An Eulerian approach to fluid\u2013structure interaction and goal-oriented mesh adaptation. Int. J. Numer. Methods Fluids 51(9\u201310), 1017\u20131039 (2006)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"2530_CR24","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1051\/m2an\/1990240404571","volume":"24","author":"M Feistauer","year":"1990","unstructured":"Feistauer, M., Sobot\u00edkov\u00e1, V.: Finite element approximation of nonlinear problems with discontinuous coefficients. ESAIM: M2AN 24, 457\u2013500 (1990)","journal-title":"ESAIM: M2AN"},{"key":"2530_CR25","volume-title":"Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System","author":"L Formaggia","year":"2010","unstructured":"Formaggia, L., Quarteroni, A., Veneziani, A.: Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, vol. 1. Springer, Berlin (2010)"},{"key":"2530_CR26","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.jcp.2019.01.028","volume":"384","author":"T Frachon","year":"2019","unstructured":"Frachon, T., Zahedi, S.: A cut finite element method for incompressible two-phase Navier\u2013Stokes flows. J. Comput. Phys. 384, 77\u201398 (2019)","journal-title":"J. Comput. Phys."},{"key":"2530_CR27","unstructured":"Frei, S.: Eulerian finite element methods for interface problems and fluid\u2013structure interactions. Ph.D. thesis, University of Heidelberg, Germany (2016)"},{"issue":"10","key":"2530_CR28","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1002\/fld.4701","volume":"89","author":"S Frei","year":"2019","unstructured":"Frei, S.: An edge-based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes. Int. J. Numer. Methods Fluids 89(10), 407\u2013429 (2019)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"3","key":"2530_CR29","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1051\/m2an\/2023022","volume":"57","author":"S Frei","year":"2023","unstructured":"Frei, S., Judakova, G., Richter, T.: A locally modified second-order finite element method for interface problems. ESAIM: M2AN 57(3), 1355\u20131380 (2023)","journal-title":"ESAIM: M2AN"},{"issue":"5","key":"2530_CR30","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1137\/130919489","volume":"52","author":"S Frei","year":"2014","unstructured":"Frei, S., Richter, T.: A locally modified parametric finite element method for interface problems. SIAM J. Numer. Anal. 52(5), 2315\u20132334 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"2530_CR31","doi-asserted-by":"crossref","first-page":"1539","DOI":"10.1051\/m2an\/2016072","volume":"51","author":"S Frei","year":"2017","unstructured":"Frei, S., Richter, T.: A second order time-stepping scheme for parabolic interface problems with moving interfaces. ESAIM: M2AN 51(4), 1539\u20131560 (2017)","journal-title":"ESAIM: M2AN"},{"issue":"3","key":"2530_CR32","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1002\/nme.2914","volume":"84","author":"T-P Fries","year":"2010","unstructured":"Fries, T.-P., Belytschko, T.: The extended\/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Methods Eng. 84(3), 253\u2013304 (2010)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"2530_CR33","first-page":"128","volume":"303","author":"S Ganesan","year":"2017","unstructured":"Ganesan, S., Srivastava, S.: ALE-SUPG finite element method for convection\u2013diffusion problems in time-dependent domains: conservative form. Appl. Math. Comput. 303, 128\u2013145 (2017)","journal-title":"Appl. Math. Comput."},{"issue":"03","key":"2530_CR34","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1142\/S0218202518500148","volume":"28","author":"H Garcke","year":"2018","unstructured":"Garcke, H., Lam, K.F., N\u00fcrnberg, R., Sitka, E.: A multiphase Cahn\u2013Hilliard\u2013Darcy model for tumour growth with necrosis. Math. Models Methods Appl. Sci. 28(03), 525\u2013577 (2018)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"2530_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-19686-7","volume-title":"Numerical Methods for Two-phase Incompressible Flows","author":"S Gross","year":"2011","unstructured":"Gross, S., Reusken, A.: Numerical Methods for Two-phase Incompressible Flows, vol. 40. Springer, Berlin (2011)"},{"issue":"12","key":"2530_CR36","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.1016\/j.cam.2009.07.041","volume":"233","author":"M Gurris","year":"2010","unstructured":"Gurris, M., Kuzmin, D., Turek, S.: Finite element simulation of compressible particle-laden gas flows. J. Comput. Appl. Math. 233(12), 3121\u20133129 (2010)","journal-title":"J. Comput. Appl. Math."},{"issue":"47\u201348","key":"2530_CR37","doi-asserted-by":"crossref","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)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR38","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.apnum.2014.06.009","volume":"85","author":"P Hansbo","year":"2014","unstructured":"Hansbo, P., Larson, M.G., Zahedi, S.: A cut finite element method for a Stokes interface problem. Appl. Numer. Math. 85, 90\u2013114 (2014)","journal-title":"Appl. Numer. Math."},{"key":"2530_CR39","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.cma.2016.04.012","volume":"307","author":"P Hansbo","year":"2016","unstructured":"Hansbo, P., Larson, M.G., Zahedi, S.: A cut finite element method for coupled bulk-surface problems on time-dependent domains. Comput. Methods Appl. Mech. Eng. 307, 96\u2013116 (2016)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"7","key":"2530_CR40","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1002\/fld.4388","volume":"85","author":"F Hecht","year":"2017","unstructured":"Hecht, F., Pironneau, O.: An energy stable monolithic Eulerian fluid\u2013structure finite element method. Int. J. Numer. Methods Fluids 85(7), 430\u2013446 (2017)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"2","key":"2530_CR41","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1006\/jcph.1997.5702","volume":"135","author":"CW Hirt","year":"1997","unstructured":"Hirt, C.W., Amsden, A.A., Cook, J.L.: An Arbitrary Lagrangian\u2013Eulerian computing method for all flow speeds. J. Comput. Phys. 135(2), 203\u2013216 (1997)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2530_CR42","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/0045-7825(81)90049-9","volume":"29","author":"TJ Hughes","year":"1981","unstructured":"Hughes, T.J., Liu, W.K., Zimmermann, T.K.: Lagrangian\u2013Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Eng. 29(3), 329\u2013349 (1981)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"11","key":"2530_CR43","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1002\/fld.1934","volume":"60","author":"S-R Hysing","year":"2009","unstructured":"Hysing, S.-R., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S., Tobiska, L.: Quantitative benchmark computations of two-dimensional bubble dynamics. Int. J. Numer. Methods Fluids 60(11), 1259\u20131288 (2009)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"1","key":"2530_CR44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40323-015-0043-7","volume":"2","author":"A Johansson","year":"2015","unstructured":"Johansson, A., Larson, M.G., Logg, A.: High order cut finite element methods for the Stokes problem. Adv. Model. Simul. Eng. Sci. 2(1), 1\u201323 (2015)","journal-title":"Adv. Model. Simul. Eng. Sci."},{"issue":"9","key":"2530_CR45","first-page":"1540","volume":"11","author":"G Judakova","year":"2017","unstructured":"Judakova, G., Bause, M.: Numerical investigation of multiphase flow in pipelines. Int. J. Mech. Mechatron. 11(9), 1540\u20131546 (2017)","journal-title":"Int. J. Mech. Mechatron."},{"issue":"267","key":"2530_CR46","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1090\/S0025-5718-08-02183-2","volume":"78","author":"M Juntunen","year":"2009","unstructured":"Juntunen, M., Stenberg, R.: Nitsche\u2019s method for general boundary conditions. Math. Comput. 78(267), 1353\u20131374 (2009)","journal-title":"Math. Comput."},{"issue":"2","key":"2530_CR47","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s00466-013-0904-1","volume":"53","author":"S Knauf","year":"2014","unstructured":"Knauf, S., Frei, S., Richter, T., Rannacher, R.: Towards a complete numerical description of lubricant film dynamics in ball bearings. Comput. Mech. 53(2), 239\u2013255 (2014)","journal-title":"Comput. Mech."},{"issue":"1","key":"2530_CR48","doi-asserted-by":"crossref","first-page":"A245","DOI":"10.1137\/130943534","volume":"37","author":"C Lehrenfeld","year":"2015","unstructured":"Lehrenfeld, C.: The Nitsche XFEM-DG space\u2013time method and its implementation in three space dimensions. SIAM J. Sci. Comput. 37(1), A245\u2013A270 (2015)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"2530_CR49","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1051\/m2an\/2018068","volume":"53","author":"C Lehrenfeld","year":"2019","unstructured":"Lehrenfeld, C., Olshanskii, M.A.: An finite element method for PDEs in time-dependent domains. ESAIM: M2AN 53(2), 585\u2013614 (2019)","journal-title":"ESAIM: M2AN"},{"issue":"4","key":"2530_CR50","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1137\/21M142126X","volume":"60","author":"Y Lou","year":"2022","unstructured":"Lou, Y., Lehrenfeld, C.: Isoparametric unfitted BDF-finite element method for PDEs on evolving domains. SIAM J. Numer. Anal. 60(4), 2069\u20132098 (2022)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"2530_CR51","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1007\/s10915-014-9838-9","volume":"61","author":"A Massing","year":"2014","unstructured":"Massing, A., Larson, M.G., Logg, A., Rognes, M.E.: A stabilized Nitsche fictitious domain method for the Stokes problem. J. Sci. Comput. 61(3), 604\u2013628 (2014)","journal-title":"J. Sci. Comput."},{"key":"2530_CR52","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.cma.2017.09.003","volume":"328","author":"A Massing","year":"2018","unstructured":"Massing, A., Schott, B., Wall, W.A.: A stabilized Nitsche cut finite element method for the Oseen problem. Comput. Methods Appl. Mech. Eng. 328, 262\u2013300 (2018)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR53","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02995904","volume":"36","author":"JA Nitsche","year":"1970","unstructured":"Nitsche, J.A.: \u00dcber ein Variationsprinzip zur L\u00f6sung von Dirichlet-Problemen bei Verwendung von Teilr\u00e4umen, die keinen Randbedingungen unterworfen sind. Abh Math Univ Hamburg 36, 9\u201315 (1970)","journal-title":"Abh Math Univ Hamburg"},{"issue":"2","key":"2530_CR54","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/0021-9991(72)90065-4","volume":"10","author":"CS Peskin","year":"1972","unstructured":"Peskin, C.S.: Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10(2), 252\u2013271 (1972)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2530_CR55","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10546-019-00473-0","volume":"174","author":"F Port\u00e9-Agel","year":"2020","unstructured":"Port\u00e9-Agel, F., Bastankhah, M., Shamsoddin, S.: Wind-turbine and wind-farm flows: a review. Bound. Layer Meteorol. 174(1), 1\u201359 (2020)","journal-title":"Bound. Layer Meteorol."},{"key":"2530_CR56","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-63970-3","volume-title":"Fluid\u2013Structure Interactions: Models, Analysis and Finite Elements","author":"T Richter","year":"2017","unstructured":"Richter, T.: Fluid\u2013Structure Interactions: Models, Analysis and Finite Elements, vol. 118. Springer, Berlin (2017)"},{"key":"2530_CR57","unstructured":"Schott, B.: Stabilized cut finite element methods for complex interface coupled flow problems. Ph.D. thesis, Technische Universit\u00e4t M\u00fcnchen (2017)"},{"issue":"2","key":"2530_CR58","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s10543-019-00783-2","volume":"60","author":"S Srivastava","year":"2020","unstructured":"Srivastava, S., Ganesan, S.: Local projection stabilization with discontinuous Galerkin method in time applied to convection dominated problems in time-dependent domains. BIT Numer. Math. 60(2), 481\u2013507 (2020)","journal-title":"BIT Numer. Math."},{"issue":"3\u20134","key":"2530_CR59","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/S0045-7825(00)00208-5","volume":"190","author":"K Stein","year":"2000","unstructured":"Stein, K., Benney, R., Kalro, V., Tezduyar, T.E., Leonard, J., Accorsi, M.: Parachute fluid\u2013structure interactions: 3-d computation. Comput. Methods Appl. Mech. Eng. 190(3\u20134), 373\u2013386 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2530_CR60","volume-title":"Galerkin Finite Element Methods for Parabolic Problems","author":"V Thom\u00e9e","year":"2007","unstructured":"Thom\u00e9e, V.: Galerkin Finite Element Methods for Parabolic Problems, vol. 25. Springer, Berlin (2007)"},{"issue":"3","key":"2530_CR61","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1023\/B:ENGI.0000007985.17625.43","volume":"47","author":"FN Van de Vosse","year":"2003","unstructured":"Van de Vosse, F.N., De Hart, J., Van Oijen, C.H.G.A., Bessems, D., Gunther, T.W.M., Segal, A., Wolters, B.J.B.M., Stijnen, J.M.A., Baaijens, F.P.T.: Finite-element-based computational methods for cardiovascular fluid\u2013structure interaction. J. Eng. Math. 47(3), 335\u2013368 (2003)","journal-title":"J. Eng. Math."},{"key":"2530_CR62","doi-asserted-by":"crossref","unstructured":"von Wahl, H.,\u00a0Richter, T.,\u00a0Lehrenfeld, C.: An unfitted finite element method for the time-dependent Stokes problem on moving domains. IMA J. Numer. Anal. 1\u201340 (2021)","DOI":"10.1093\/imanum\/drab044"},{"issue":"5","key":"2530_CR63","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1002\/fld.1763","volume":"57","author":"WA Wall","year":"2008","unstructured":"Wall, W.A., Rabczuk, T.: Fluid\u2013structure interaction in lower airways of CT-based lung geometries. Int. J. Numer. Methods Fluids 57(5), 653\u2013675 (2008)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"2530_CR64","unstructured":"Williams, T.,\u00a0Kelley, C.,\u00a0Bersch, C., Br\u00f6ker, H.-B.,\u00a0Campbell, J.,\u00a0Cunningham, R.,\u00a0Denholm, D.,\u00a0Elber, G.,\u00a0Fearick, R.,\u00a0Grammes, C., et\u00a0al.: gnuplot 5.2. An interactive plotting program. Available online: http:\/\/www.gnuplot.info\/docs_5, 2 (2017)"},{"key":"2530_CR65","doi-asserted-by":"crossref","unstructured":"Zahedi, S.: A space-time cut finite element method with quadrature in time. In: Geometrically Unfitted Finite Element Methods and Applications: Proceedings of the UCL Workshop 2016, pp. 281\u2013306. Springer International Publishing (2017)","DOI":"10.1007\/978-3-319-71431-8_9"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02530-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02530-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02530-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,23]],"date-time":"2024-05-23T14:13:02Z","timestamp":1716473582000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02530-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,22]]},"references-count":65,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2530"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02530-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,22]]},"assertion":[{"value":"28 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose and there are no Conflict of interest that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial or non-financial interest in the subject matter or materials discussed in this manuscript. Moreover, we have no financial or proprietary interests in any material discussed in this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"64"}}