{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:30:51Z","timestamp":1758709851578},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T00:00:00Z","timestamp":1491696000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s10915-017-0430-y","type":"journal-article","created":{"date-parts":[[2017,4,9]],"date-time":"2017-04-09T08:51:34Z","timestamp":1491727894000},"page":"197-219","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models"],"prefix":"10.1007","volume":"74","author":[{"given":"Immanuel","family":"Martini","sequence":"first","affiliation":[]},{"given":"Bernard","family":"Haasdonk","sequence":"additional","affiliation":[]},{"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,4,9]]},"reference":[{"key":"430_CR1","volume-title":"Theory of Wing Sections","author":"I Abbott","year":"1959","unstructured":"Abbott, I., von Doenhoff, A.: Theory of Wing Sections. Dover Publications, New York (1959)"},{"issue":"339","key":"430_CR2","first-page":"667","volume":"I","author":"M Barrault","year":"2004","unstructured":"Barrault, M., Maday, Y., Nguyen, N., Patera, A.: An \u201cempirical interpolation\u201d method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Acad. Sci. Ser. I(339), 667\u2013672 (2004)","journal-title":"Comptes Rendus Acad. Sci. Ser."},{"key":"430_CR3","unstructured":"Benner, P., Feng, L.: Model order reduction for coupled problems. Tech. Rep. MPIMD\/15-02, Max Planck Institue for Dynamics of Complex Technical Systems, Magdeburg (2015)"},{"issue":"3","key":"430_CR4","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1137\/100795772","volume":"43","author":"P Binev","year":"2011","unstructured":"Binev, P., Cohen, A., Dahmen, W., DeVore, R., Petrova, G., Wojtaszczyk, P.: Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43(3), 1457\u20131472 (2011)","journal-title":"SIAM J. Math. Anal."},{"key":"430_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01395985","volume":"36","author":"F Brezzi","year":"1980","unstructured":"Brezzi, F., Rappaz, J., Raviart, P.: Finite dimensional approximation of nonlinear problems. Part I: branches of nonsingular solutions. Numer. Math. 36, 1\u201325 (1980)","journal-title":"Numer. Math."},{"key":"430_CR6","unstructured":"Buhr, A., Engwer, C., Ohlberger, M., Rave, S.: A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations. In: Proceedings of the 11th World Congress on Computational Mechanics CIMNE, Barcelona, pp. 4094\u20134102 (2014)"},{"key":"430_CR7","first-page":"487","volume-title":"Handbook of Numerical Analysis","author":"G Caloz","year":"1997","unstructured":"Caloz, G., Rappaz, J.: Numerical analysis for nonlinear and bifurcation problems. In: Ciarlet, P., Lions, J. (eds.) Handbook of Numerical Analysis, pp. 487\u2013637. Elsevier, Amsterdam (1997)"},{"issue":"1","key":"430_CR8","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1007\/s10915-011-9478-2","volume":"50","author":"S Deparis","year":"2012","unstructured":"Deparis, S., L\u00f8vgren, E.: Stabilized reduced basis approximation of incompressible three-dimensional Navier\u2013Stokes equations in parametrized deformed domains. J. Sci. Comput. 50(1), 198\u2013212 (2012)","journal-title":"J. Sci. Comput."},{"key":"430_CR9","unstructured":"Dinh, Q., Glowinski, R., P\u00e9riaux, J., Terrasson, G.: On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition. In: Domain Decomposition Methods for Partial Differential Equations, pp. 350\u2013369. SIAM, Philadelphia (1988)"},{"issue":"2","key":"430_CR10","doi-asserted-by":"crossref","first-page":"315","DOI":"10.5209\/rev_REMA.2009.v22.n2.16263","volume":"22","author":"M Discacciati","year":"2009","unstructured":"Discacciati, M., Quarteroni, A.: Navier\u2013Stokes\/Darcy coupling: modeling, analysis, and numerical approximation. Rev. Mat. Complut. 22(2), 315\u2013426 (2009)","journal-title":"Rev. Mat. Complut."},{"issue":"5","key":"430_CR11","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1002\/nme.4543","volume":"96","author":"J Eftang","year":"2013","unstructured":"Eftang, J., Patera, A.: Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Int. J. Numer. Methods Eng. 96(5), 269\u2013302 (2013). doi: 10.1002\/nme.4543","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"5","key":"430_CR12","doi-asserted-by":"crossref","first-page":"A2812","DOI":"10.1137\/110854084","volume":"34","author":"A Gerner","year":"2012","unstructured":"Gerner, A., Veroy, K.: Certified reduced basis methods for parametrized saddle point problems. SIAM J. Sci. Comput. 34(5), A2812\u2013A2836 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"430_CR13","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1016\/j.camwa.2005.08.009","volume":"50","author":"L Giraud","year":"2005","unstructured":"Giraud, L., Langou, J., Rozloznik, M.: The loss of orthogonality in the Gram-Schmidt orthogonalization process. Comput. Math. Appl. 50, 1069\u20131075 (2005)","journal-title":"Comput. Math. Appl."},{"key":"430_CR14","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61623-5","volume-title":"Finite Element Methods for Navier\u2013Stokes Equations: Theory and Algorithms","author":"V Girault","year":"1986","unstructured":"Girault, V., Raviart, P.A.: Finite Element Methods for Navier\u2013Stokes Equations: Theory and Algorithms. Springer Series in Computational Mathematics. Springer, Berlin (1986)"},{"key":"430_CR15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1051\/m2an:2005006","volume":"39","author":"M Grepl","year":"2005","unstructured":"Grepl, M., Patera, A.: A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. Math. Model. Numer. Anal. 39, 157\u2013181 (2005)","journal-title":"Math. Model. Numer. Anal."},{"key":"430_CR16","unstructured":"Haasdonk, B., Ohlberger, M.: Adaptive basis enrichment for the reduced basis method applied to finite volume schemes. In: Proceedings of 5th International Symposium on Finite Volumes for Complex Applications, pp. 471\u2013478 (2008)"},{"key":"430_CR17","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1051\/m2an:2008001","volume":"42","author":"B Haasdonk","year":"2008","unstructured":"Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. Math. Model. Numer. Anal. 42, 277\u2013302 (2008)","journal-title":"Math. Model. Numer. Anal."},{"key":"430_CR18","series-title":"SpringerBriefs in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-22470-1","volume-title":"Certified Reduced Basis Methods for Parametrized Partial Differential Equations","author":"J Hesthaven","year":"2016","unstructured":"Hesthaven, J., Rozza, G., Stamm, B.: Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer, Berlin (2016)"},{"key":"430_CR19","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1016\/j.cma.2010.02.011","volume":"199","author":"D Huynh","year":"2010","unstructured":"Huynh, D., Knezevic, D., Chen, Y., Hesthaven, J., Patera, A.: A natural-norm successive constraint method for inf-sup lower bounds. Comput. Methods Appl. Mech. Eng. 199, 1963\u20131975 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"430_CR20","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1051\/m2an\/2012022","volume":"47","author":"D Huynh","year":"2013","unstructured":"Huynh, D., Knezevic, D., Patera, A.: A static condensation reduced basis element method: approximation and a posteriori error estimation. Math. Model. Numer. Anal. 47(1), 213\u2013251 (2013)","journal-title":"Math. Model. Numer. Anal."},{"issue":"345","key":"430_CR21","first-page":"473","volume":"I","author":"D Huynh","year":"2007","unstructured":"Huynh, D., Rozza, G., Sen, S., Patera, A.: A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. Comptes Rendus Acad. Sci. Ser. I(345), 473\u2013478 (2007)","journal-title":"Comptes Rendus Acad. Sci. Ser."},{"issue":"1","key":"430_CR22","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.camwa.2015.12.001","volume":"71","author":"L Iapichino","year":"2016","unstructured":"Iapichino, L., Quarteroni, A., Rozza, G.: Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries. Comput. Math. Appl. 71(1), 408\u2013430 (2016)","journal-title":"Comput. Math. Appl."},{"key":"430_CR23","first-page":"62","volume":"221\u2013222","author":"L Iapichino","year":"2012","unstructured":"Iapichino, L., Quarteroni, A., Rozza, G.: A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Comput. Methods Appl. Mech. Eng. 221\u2013222, 62\u201382 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"430_CR24","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1002\/fld.377","volume":"40","author":"V John","year":"2002","unstructured":"John, V.: Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier\u2013Stokes equations. Int. J. Numer. Methods Fluids 40, 775\u2013798 (2002). doi: 10.1002\/fld.377","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"430_CR25","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1051\/m2an:2006021","volume":"40","author":"A L\u00f8vgren","year":"2006","unstructured":"L\u00f8vgren, A., Maday, Y., R\u00f8nquist, E.: A reduced basis element method for the steady Stokes problem. Math. Model. Numer. Anal. 40, 529\u2013552 (2006)","journal-title":"Math. Model. Numer. Anal."},{"key":"430_CR26","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1023\/A:1015197908587","volume":"17","author":"Y Maday","year":"2002","unstructured":"Maday, Y., R\u00f8nquist, E.: A reduced-basis element method. J. Sci. Comput. 17, 447\u2013459 (2002)","journal-title":"J. Sci. Comput."},{"key":"430_CR27","first-page":"240","volume":"26","author":"Y Maday","year":"2004","unstructured":"Maday, Y., R\u00f8nquist, E.: The reduced basis element method: application to a thermal fin problem. J. Sci. Comput. 26, 240\u2013258 (2004)","journal-title":"J. Sci. Comput."},{"key":"430_CR28","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.apnum.2013.12.001","volume":"78","author":"I Maier","year":"2014","unstructured":"Maier, I., Haasdonk, B.: A Dirichlet\u2013Neumann reduced basis method for homogeneous domain decomposition problems. Appl. Numer. Math. 78, 31\u201348 (2014). doi: 10.1016\/j.apnum.2013.12.001","journal-title":"Appl. Numer. Math."},{"key":"430_CR29","unstructured":"Manzoni, A.: Reduced models for optimal control, shape optimization and inverse problems in haemodynamics. Ph.D. thesis, EPFL, Lausanne (2012)"},{"issue":"4","key":"430_CR30","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1051\/m2an\/2014013","volume":"48","author":"A Manzoni","year":"2014","unstructured":"Manzoni, A.: An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier\u2013Stokes flows. Math. Model. Numer. Anal. 48(4), 1199\u20131226 (2014)","journal-title":"Math. Model. Numer. Anal."},{"issue":"5","key":"430_CR31","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1007\/s10444-015-9413-4","volume":"41","author":"A Manzoni","year":"2015","unstructured":"Manzoni, A., Negri, F.: Rigorous and heuristic strategies for the approximation of stability factors in nonlinear parametrized PDEs. Adv. Comput. Math. 41(5), 1255\u20131288 (2015). doi: 10.1007\/s10444-015-9413-4","journal-title":"Adv. Comput. Math."},{"key":"430_CR32","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.cma.2014.11.037","volume":"284","author":"A Manzoni","year":"2015","unstructured":"Manzoni, A., Salmoiraghi, F., Heltai, L.: Reduced basis isogeometric methods (RB-IGA) for the real-time simultion of potential flows about parametrized NACA airfoils. Comput. Methods Appl. Mech. Eng. 284, 1147\u20131180 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"430_CR33","doi-asserted-by":"publisher","unstructured":"Martini, I., Haasdonk, B.: Output error bounds for the Dirichlet\u2013Neumann reduced basis method. In: Numerical Mathematics and Advanced Applications-ENUMATH 2013, Lecture Notes in Computational Science and Engineering, vol. 103, pp. 437\u2013445 (2015). doi: 10.1007\/978-3-319-10705-9_43","DOI":"10.1007\/978-3-319-10705-9_43"},{"issue":"5","key":"430_CR34","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1007\/s10444-014-9396-6","volume":"41","author":"I Martini","year":"2015","unstructured":"Martini, I., Rozza, G., Haasdonk, B.: Reduced basis approximation and a-posteriori error estimation for the coupled Stokes\u2013Darcy system. Adv. Comput. Math. 41(5), 1131\u20131157 (2015). doi: 10.1007\/s10444-014-9396-6","journal-title":"Adv. Comput. Math."},{"key":"430_CR35","volume-title":"Incompressible Flow","author":"R Panton","year":"1996","unstructured":"Panton, R.: Incompressible Flow. Wiley, Hoboken (1996)"},{"key":"430_CR36","unstructured":"Patera, A., Rozza, G.: Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. MIT Pappalardo Graduate Monographs in Mechanical Engineering (2007). http:\/\/augustine.mit.edu"},{"key":"430_CR37","doi-asserted-by":"publisher","unstructured":"Pitton, G., Rozza, G.: On the application of reduced basis methods to bifurcation problems in incompressible fluid dynamics. J. Sci. Comput. (2017). doi: 10.1007\/s10915-017-0419-6","DOI":"10.1007\/s10915-017-0419-6"},{"key":"430_CR38","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1186\/2190-5983-1-3","volume":"1","author":"A Quarteroni","year":"2011","unstructured":"Quarteroni, A., Rozza, G., Manzoni, A.: Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Ind. 1, 3 (2011). doi: 10.1186\/2190-5983-1-3","journal-title":"J. Math. Ind."},{"key":"430_CR39","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1007\/BF01385813","volume":"59","author":"A Quarteroni","year":"1991","unstructured":"Quarteroni, A., Sacchi Landriani, G., Valli, A.: Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements. Numer. Math. 59, 831\u2013859 (1991)","journal-title":"Numer. Math."},{"key":"430_CR40","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198501787.001.0001","volume-title":"Domain Decomposition Methods for Partial Differential Equations","author":"A Quarteroni","year":"1999","unstructured":"Quarteroni, A., Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, Oxford (1999)"},{"key":"430_CR41","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s00211-013-0534-8","volume":"125","author":"G Rozza","year":"2013","unstructured":"Rozza, G., Huynh, D., Manzoni, A.: Reduced basis approximation and a posteriori error estimation for Stokes flow in parametrized geometries: roles of the inf-sup stability constants. Numer. Math. 125, 115\u2013152 (2013)","journal-title":"Numer. Math."},{"key":"430_CR42","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11831-008-9019-9","volume":"15","author":"G Rozza","year":"2008","unstructured":"Rozza, G., Huynh, D., Patera, A.T.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15, 229\u2013275 (2008)","journal-title":"Arch. Comput. Methods Eng."},{"key":"430_CR43","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1016\/j.cma.2006.09.005","volume":"196","author":"G Rozza","year":"2007","unstructured":"Rozza, G., Veroy, K.: On the stability of the reduced basis method for Stokes equations in parametrized domains. Comput. Methods Appl. Mech. Eng. 196, 1244\u20131260 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"430_CR44","first-page":"239","volume-title":"Numerical Methods for the Navier\u2013Stokes Equations","author":"K Schenk","year":"1993","unstructured":"Schenk, K., Hebeker, F.: Coupling of two-dimensional viscous and inviscid incompressible stokes equations. In: Hebeker, F., Rannacher, R., Wittum, G. (eds.) Numerical Methods for the Navier\u2013Stokes Equations, pp. 239\u2013248. Springer Fachmedien Wiesbaden, Wiesbaden (1993)"},{"key":"430_CR45","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.cma.2014.09.020","volume":"283","author":"K Smetana","year":"2015","unstructured":"Smetana, K.: A new certification framework for the port reduced static condensation reduced basis element method. Comput. Methods Appl. Mech. Eng. 283, 352\u2013383 (2015)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"430_CR46","doi-asserted-by":"crossref","unstructured":"Temam, R.: Navier\u2013Stokes Equations: Theory and Numerical Analysis. AMS Chelsea Publishing, Providence (2001)","DOI":"10.1090\/chel\/343"},{"issue":"3","key":"430_CR47","doi-asserted-by":"crossref","first-page":"B294","DOI":"10.1137\/120887709","volume":"36","author":"S Vallagh\u00e9","year":"2013","unstructured":"Vallagh\u00e9, S., Patera, A.: The static condensation reduced basis element method for a mixed-mean conjugate heat exchanger model. SIAM J. Sci. Comput. 36(3), B294\u2013B320 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"430_CR48","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1002\/fld.867","volume":"47","author":"K Veroy","year":"2005","unstructured":"Veroy, K., Patera, A.: Certified real-time solution of the parametrized steady incompressible Navier\u2013Stokes equations: rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Methods Fluids 47, 773\u2013788 (2005)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"430_CR49","doi-asserted-by":"crossref","unstructured":"Veroy, K., Prud\u2019homme, C., Rovas, D., Patera, A.: A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations. In: Proceedings of 16th AIAA Computational Fluid Dynamics Conference, p. 3847 (2003)","DOI":"10.2514\/6.2003-3847"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0430-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0430-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0430-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T13:56:52Z","timestamp":1719151012000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0430-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,9]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["430"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0430-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,9]]}}}