{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T23:02:19Z","timestamp":1763852539169,"version":"3.37.3"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"European Research Council","award":["681447"],"award-info":[{"award-number":["681447"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s10915-020-01232-x","type":"journal-article","created":{"date-parts":[[2020,6,6]],"date-time":"2020-06-06T10:02:31Z","timestamp":1591437751000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["POD\u2013Galerkin Model Order Reduction for Parametrized Time Dependent Linear Quadratic Optimal Control Problems in Saddle Point Formulation"],"prefix":"10.1007","volume":"83","author":[{"given":"Maria","family":"Strazzullo","sequence":"first","affiliation":[]},{"given":"Francesco","family":"Ballarin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0810-8812","authenticated-orcid":false,"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,6]]},"reference":[{"key":"1232_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2020.03.019","author":"S Ali","year":"2020","unstructured":"Ali, S., Ballarin, F., Rozza, G.: Stabilized reduced basis methods for parametrized steady Stokes and Navier-Stokes equations. Comput. Math. Appl. (2020). https:\/\/doi.org\/10.1016\/j.camwa.2020.03.019","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"1232_CR2","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1007\/BF02165003","volume":"16","author":"I Babu\u0161ka","year":"1971","unstructured":"Babu\u0161ka, I.: Error-bounds for finite element method. Numer. Math. 16(4), 322\u2013333 (1971). https:\/\/doi.org\/10.1007\/BF02165003","journal-title":"Numer. Math."},{"issue":"6","key":"1232_CR3","doi-asserted-by":"publisher","first-page":"A3921","DOI":"10.1137\/16M1059898","volume":"38","author":"E Bader","year":"2016","unstructured":"Bader, E., K\u00e4rcher, M., Grepl, M.A., Veroy, K.: Certified reduced basis methods for parametrized distributed elliptic optimal control problems with control constraints. SIAM J. Sci. Comput. 38(6), A3921\u2013A3946 (2016)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"1232_CR4","doi-asserted-by":"publisher","first-page":"719","DOI":"10.1016\/j.ifacol.2015.05.167","volume":"48","author":"E Bader","year":"2015","unstructured":"Bader, E., K\u00e4rcher, M., Grepl, M.A., Veroy-Grepl, K.: A certified reduced basis approach for parametrized linear-quadratic optimal control problems with control constraints. IFAC-PapersOnLine 48(1), 719\u2013720 (2015)","journal-title":"IFAC-PapersOnLine"},{"issue":"4","key":"1232_CR5","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1007\/s10237-017-0893-7","volume":"16","author":"F Ballarin","year":"2017","unstructured":"Ballarin, F., Faggiano, E., Manzoni, A., Quarteroni, A., Rozza, G., Ippolito, S., Antona, C., Scrofani, R.: Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts. Biomech. Model. Mechanobiol. 16(4), 1373\u20131399 (2017). https:\/\/doi.org\/10.1007\/s10237-017-0893-7","journal-title":"Biomech. Model. Mechanobiol."},{"issue":"5","key":"1232_CR6","doi-asserted-by":"publisher","first-page":"1136","DOI":"10.1002\/nme.4772","volume":"102","author":"F Ballarin","year":"2015","unstructured":"Ballarin, F., Manzoni, A., Quarteroni, A., Rozza, G.: Supremizer stabilization of POD\u2013Galerkin approximation of parametrized steady incompressible Navier\u2013Stokes equations. Int. J. Numer. Methods Eng. 102(5), 1136\u20131161 (2015)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"9","key":"1232_CR7","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.crma.2004.08.006","volume":"339","author":"M Barrault","year":"2004","unstructured":"Barrault, M., Maday, Y., Nguyen, N.C., Patera, A.T.: An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339(9), 667\u2013672 (2004)","journal-title":"C. R. Math."},{"key":"1232_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1\u2013137 (2005). https:\/\/doi.org\/10.1017\/S0962492904000212","journal-title":"Acta Numer."},{"key":"1232_CR9","volume-title":"Least-Squares Finite Element Methods","author":"PB Bochev","year":"2009","unstructured":"Bochev, P.B., Gunzburger, M.D.: Least-Squares Finite Element Methods, vol. 166. Springer, New York (2009)"},{"key":"1232_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5","volume-title":"Mixed Finite Element Methods and Applications","author":"D Boffi","year":"2013","unstructured":"Boffi, D., Brezzi, F., Fortin, M.: Mixed Finite Element Methods and Applications, vol. 44. Springer, Berlin (2013)"},{"issue":"R2","key":"1232_CR11","first-page":"129","volume":"8","author":"F Brezzi","year":"1974","unstructured":"Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. ESAIM Math. Model. Numer. Anal. 8(R2), 129\u2013151 (1974)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"1\u20133","key":"1232_CR12","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1016\/j.cma.2006.04.004","volume":"196","author":"J Burkardt","year":"2006","unstructured":"Burkardt, J., Gunzburger, M., Lee, H.: POD and CVT-based reduced-order modeling of Navier\u2013Stokes flows. Comput. Methods Appl. Mech. Eng. 196(1\u20133), 337\u2013355 (2006)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"6","key":"1232_CR13","doi-asserted-by":"publisher","first-page":"1821","DOI":"10.1051\/m2an\/2013090","volume":"47","author":"D Chapelle","year":"2013","unstructured":"Chapelle, D., Gariah, A., Moireau, P., Sainte-Marie, J.: A Galerkin strategy with proper orthogonal decomposition for parameter-dependent problems: analysis, assessments and applications to parameter estimation. ESAIM Math. Model. Numer. Anal. 47(6), 1821\u20131843 (2013)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"1232_CR14","doi-asserted-by":"crossref","unstructured":"De los Reyes, J.C., Tr\u00f6ltzsch, F.: Optimal control of the stationary Navier\u2013Stokes equations with mixed control-state constraints. SIAM J. Control Optim. 46(2), 604\u2013629 (2007)","DOI":"10.1137\/050646949"},{"issue":"4","key":"1232_CR15","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1002\/fld.1464","volume":"55","author":"L Ded\u00e8","year":"2007","unstructured":"Ded\u00e8, L.: Optimal flow control for Navier\u2013Stokes equations: drag minimization. Int. J. Numer. Methods Fluids 55(4), 347\u2013366 (2007)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"2","key":"1232_CR16","doi-asserted-by":"publisher","first-page":"997","DOI":"10.1137\/090760453","volume":"32","author":"L Ded\u00e8","year":"2010","unstructured":"Ded\u00e8, L.: Reduced basis method and a posteriori error estimation for parametrized linear-quadratic optimal control problems. SIAM J. Sci. Comput. 32(2), 997\u20131019 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"1232_CR17","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719826","volume-title":"Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization","author":"MC Delfour","year":"2011","unstructured":"Delfour, M.C., Zol\u00e9sio, J.: Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, vol. 22. SIAM, Philadelphia (2011)"},{"issue":"1","key":"1232_CR18","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1137\/0724002","volume":"24","author":"K Eriksson","year":"1987","unstructured":"Eriksson, K., Johnson, C.: Error estimates and automatic time step control for nonlinear parabolic problems. I. SIAM J. Numer. Anal. 24(1), 12\u201323 (1987)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"1232_CR19","doi-asserted-by":"publisher","first-page":"A2812","DOI":"10.1137\/110854084","volume":"34","author":"AL Gerner","year":"2012","unstructured":"Gerner, A.L., 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":"1232_CR20","first-page":"1","volume-title":"Two Ways to Treat Time in Reduced Basis Methods","author":"S Glas","year":"2017","unstructured":"Glas, S., Mayerhofer, A., Urban, K.: Two Ways to Treat Time in Reduced Basis Methods, pp. 1\u201316. Springer, Cham (2017)"},{"issue":"3","key":"1232_CR21","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1051\/m2an\/2013124","volume":"48","author":"R Guberovic","year":"2014","unstructured":"Guberovic, R., Schwab, C., Stevenson, R.: Space-time variational saddle point formulations of stokes and Navier\u2013Stokes equations. ESAIM Math. Model. Numer. Anal. 48(3), 875\u2013894 (2014). https:\/\/doi.org\/10.1051\/m2an\/2013124","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"1232_CR22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718690","volume-title":"Introduction to Shape Optimization: Theory, Approximation, and Computation","author":"J Haslinger","year":"2003","unstructured":"Haslinger, J., M\u00e4kinen, R.A.E.: Introduction to Shape Optimization: Theory, Approximation, and Computation. SIAM, Philadelphia (2003)"},{"key":"1232_CR23","volume-title":"Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer Briefs in Mathematics","author":"JS Hesthaven","year":"2015","unstructured":"Hesthaven, J.S., Rozza, G., Stamm, B.: Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer Briefs in Mathematics. Springer, Milan (2015)"},{"key":"1232_CR24","unstructured":"Hinze, M., K\u00f6ster, M., Turek, S.: A hierarchical space-time solver for distributed control of the Stokes equation. Technical Report, SPP1253-16-01 (2008)"},{"key":"1232_CR25","volume-title":"Optimization with PDE Constraints","author":"M Hinze","year":"2008","unstructured":"Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.: Optimization with PDE Constraints, vol. 23. Springer, Antwerp (2008)"},{"key":"1232_CR26","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/978-3-319-39929-4_37","volume-title":"Numerical Mathematics and Advanced Applications ENUMATH 2015","author":"L Iapichino","year":"2016","unstructured":"Iapichino, L., Trenz, S., Volkwein, S.: Reduced-order multiobjective optimal control of semilinear parabolic problems. In: Karas\u00f6zen, B., Manguo\u011flu, M., Tezer-Sezgin, M., G\u00f6ktepe, S., U\u011fur, \u00d6. (eds.) Numerical Mathematics and Advanced Applications ENUMATH 2015, pp. 389\u2013397. Springer, Cham (2016)"},{"issue":"5","key":"1232_CR27","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1007\/s10444-016-9512-x","volume":"43","author":"L Iapichino","year":"2017","unstructured":"Iapichino, L., Ulbrich, S., Volkwein, S.: Multiobjective PDE-constrained optimization using the reduced-basis method. Adv. Comput. Math. 43(5), 945\u2013972 (2017). https:\/\/doi.org\/10.1007\/s10444-016-9512-x","journal-title":"Adv. Comput. Math."},{"issue":"2","key":"1232_CR28","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1051\/cocv\/2013069","volume":"20","author":"M K\u00e4rcher","year":"2014","unstructured":"K\u00e4rcher, M., Grepl, M.A.: A certified reduced basis method for parametrized elliptic optimal control problems. ESAIM Control Optim. Calc. Var. 20(2), 416\u2013441 (2014)","journal-title":"ESAIM Control Optim. Calc. Var."},{"issue":"1","key":"1232_CR29","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/s10915-017-0539-z","volume":"75","author":"M K\u00e4rcher","year":"2018","unstructured":"K\u00e4rcher, M., Tokoutsi, Z., Grepl, M.A., Veroy, K.: Certified reduced basis methods for parametrized elliptic optimal control problems with distributed controls. J. Sci. Comput. 75(1), 276\u2013307 (2018)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1232_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1051\/m2an:2007054","volume":"42","author":"K Kunisch","year":"2008","unstructured":"Kunisch, K., Volkwein, S.: Proper orthogonal decomposition for optimality systems. ESAIM Math. Model. Numer. Anal. 42(1), 1\u201323 (2008)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"7","key":"1232_CR31","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1002\/cnm.2559","volume":"29","author":"T Lassila","year":"2013","unstructured":"Lassila, T., Manzoni, A., Quarteroni, A., Rozza, G.: A reduced computational and geometrical framework for inverse problems in hemodynamics. Int. J. Numer. Methods Biomed. Eng. 29(7), 741\u2013776 (2013). https:\/\/doi.org\/10.1002\/cnm.2559","journal-title":"Int. J. Numer. Methods Biomed. Eng."},{"key":"1232_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-05083-6","volume-title":"Trends in PDE Constrained Optimization","author":"G Leugering","year":"2014","unstructured":"Leugering, G., Benner, P., Engell, S., Griewank, A., Harbrecht, H., Hinze, M., Rannacher, R., Ulbrich, S.: Trends in PDE Constrained Optimization. Springer, New York (2014)"},{"key":"1232_CR33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of System Governed by Partial Differential Equations","author":"JL Lions","year":"1971","unstructured":"Lions, J.L.: Optimal Control of System Governed by Partial Differential Equations, vol. 170. Springer, Berlin (1971)"},{"key":"1232_CR34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23099-8","volume-title":"Automated Solution of Differential Equations by the Finite Element Method","author":"A Logg","year":"2012","unstructured":"Logg, A., Mardal, K., Wells, G.: Automated Solution of Differential Equations by the Finite Element Method. Springer, Berlin (2012)"},{"key":"1232_CR35","volume-title":"Applied Shape Optimization for Fluids","author":"B Mohammadi","year":"2010","unstructured":"Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids. Oxford University Press, New York (2010)"},{"issue":"4","key":"1232_CR36","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.camwa.2014.12.010","volume":"69","author":"F Negri","year":"2015","unstructured":"Negri, F., Manzoni, A., Rozza, G.: Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations. Comput. Math. Appl. 69(4), 319\u2013336 (2015)","journal-title":"Comput. Math. Appl."},{"issue":"5","key":"1232_CR37","doi-asserted-by":"publisher","first-page":"A2316","DOI":"10.1137\/120894737","volume":"35","author":"F Negri","year":"2013","unstructured":"Negri, F., Rozza, G., Manzoni, A., Quarteroni, A.: Reduced basis method for parametrized elliptic optimal control problems. SIAM J. Sci. Comput. 35(5), A2316\u2013A2340 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1232_CR38","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1016\/j.camwa.2006.02.034","volume":"53","author":"M Po\u0161ta","year":"2007","unstructured":"Po\u0161ta, M., Roub\u00ed\u010dek, T.: Optimal control of Navier\u2013Stokes equations by Oseen approximation. Comput. Math. Appl. 53(3), 569\u2013581 (2007)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"1232_CR39","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1115\/1.1448332","volume":"124","author":"C Prud\u2019Homme","year":"2002","unstructured":"Prud\u2019Homme, C., Rovas, D.V., Veroy, K., Machiels, L., Maday, Y., Patera, A., Turinici, G.: Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124(1), 70\u201380 (2002)","journal-title":"J. Fluids Eng."},{"key":"1232_CR40","first-page":"261","volume-title":"IFIP Conference on System Modeling and Optimization, System Modeling and Optimization, CSMO","author":"A Quarteroni","year":"2005","unstructured":"Quarteroni, A., Rozza, G., Ded\u00e8, L., Quaini, A.: Numerical approximation of a control problem for advection\u2013diffusion processes. In: Ceragioli, F., Dontchev, A., Futura, H., Marti, K., Pandolfi, L. (eds.) IFIP Conference on System Modeling and Optimization, System Modeling and Optimization, CSMO, vol. 199, pp. 261\u2013273. Springer, Boston (2005)"},{"key":"1232_CR41","unstructured":"Quarteroni, A., Rozza, G., Quaini, A.: Reduced basis methods for optimal control of advection\u2013diffusion problems. In: Advances in Numerical Mathematics, pp. 193\u2013216. RAS and University of Houston, Moscow (2007)"},{"key":"1232_CR42","volume-title":"Numerical Approximation of Partial Differential Equations","author":"A Quarteroni","year":"2008","unstructured":"Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations, vol. 23. Springer, Berlin (2008)"},{"key":"1232_CR43","unstructured":"RBniCS\u2014reduced order modelling in FEniCS. http:\/\/mathlab.sissa.it\/rbnics (2015)"},{"issue":"1","key":"1232_CR44","doi-asserted-by":"publisher","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 flows in parametrized geometries: roles of the inf\u2013sup stability constants. Numer. Math. 125(1), 115\u2013152 (2013)","journal-title":"Numer. Math."},{"issue":"3","key":"1232_CR45","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s11831-008-9019-9","volume":"15","author":"G Rozza","year":"2008","unstructured":"Rozza, G., Huynh, D., Patera, A.: Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: application to transport and continuum mechanics. Arch. Comput. Methods Eng. 15(3), 229\u2013275 (2008)","journal-title":"Arch. Comput. Methods Eng."},{"key":"1232_CR46","unstructured":"Rozza, G., Manzoni, A., Negri, F.: Reduction strategies for PDE-constrained optimization problems in haemodynamics. In: ECCOMAS: Congress Proceedings, Vienna, pp. 1749\u20131768 (2012)"},{"issue":"7","key":"1232_CR47","doi-asserted-by":"publisher","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(7), 1244\u20131260 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"1232_CR48","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1137\/060660977","volume":"29","author":"J Sch\u00f6berl","year":"2007","unstructured":"Sch\u00f6berl, J., Zulehner, W.: Symmetric indefinite preconditioners for saddle point problems with applications to PDE-constrained optimisation problems. SIAM J. Matrix Anal. Appl. 29(3), 752\u2013773 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"267","key":"1232_CR49","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1090\/S0025-5718-08-02205-9","volume":"78","author":"C Schwab","year":"2009","unstructured":"Schwab, C., Stevenson, R.: Space-time adaptive wavelet methods for parabolic evolution problems. Math. Comput. 78(267), 1293\u20131318 (2009)","journal-title":"Math. Comput."},{"key":"1232_CR50","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.cam.2013.11.006","volume":"261","author":"ZK Seymen","year":"2014","unstructured":"Seymen, Z.K., Y\u00fccel, H., Karas\u00f6zen, B.: Distributed optimal control of time-dependent diffusion\u2013convection\u2013reaction equations using space-time discretization. J. Comput. Appl. Math. 261, 146\u2013157 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"1232_CR51","unstructured":"Stoll, M., Wathen, A.: All-at-once solution of time-dependent PDE-constrained optimization problems. Unspecified, Tech. Rep (2010)"},{"issue":"1","key":"1232_CR52","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.jcp.2012.08.039","volume":"232","author":"M Stoll","year":"2013","unstructured":"Stoll, M., Wathen, A.: All-at-once solution of time-dependent Stokes control. J. Comput. Phys. 232(1), 498\u2013515 (2013). https:\/\/doi.org\/10.1016\/j.jcp.2012.08.039","journal-title":"J. Comput. Phys."},{"issue":"4","key":"1232_CR53","doi-asserted-by":"publisher","first-page":"B1055","DOI":"10.1137\/17M1150591","volume":"40","author":"M Strazzullo","year":"2018","unstructured":"Strazzullo, M., Ballarin, F., Mosetti, R., Rozza, G.: Model reduction for parametrized optimal control problems in environmental marine sciences and engineering. SIAM J. Sci. Comput. 40(4), B1055\u2013B1079 (2018). https:\/\/doi.org\/10.1137\/17M1150591","journal-title":"SIAM J. Sci. Comput."},{"key":"1232_CR54","doi-asserted-by":"crossref","unstructured":"Strazzullo, M., Zainib, Z., Ballarin, F., Rozza, G.: Reduced order methods for parametrized nonlinear and time dependent optimal flow control problems: towards applications in biomedical and environmental sciences. ENUMATH 2019 Proceedings (2020)","DOI":"10.1007\/978-3-030-55874-1_83"},{"key":"1232_CR55","doi-asserted-by":"crossref","unstructured":"Tr\u00f6ltzsch, F.: Optimal Control of Partial Differential Equations. Graduate Studies in Mathematics, vol. 112. Verlag, Wiesbad (2010)","DOI":"10.1090\/gsm\/112"},{"issue":"3\u20134","key":"1232_CR56","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.crma.2012.01.026","volume":"350","author":"K Urban","year":"2012","unstructured":"Urban, K., Patera, A.T.: A new error bound for reduced basis approximation of parabolic partial differential equations. C. R. Math. 350(3\u20134), 203\u2013207 (2012)","journal-title":"C. R. Math."},{"issue":"1","key":"1232_CR57","doi-asserted-by":"publisher","first-page":"A232","DOI":"10.1137\/120903300","volume":"36","author":"M Yano","year":"2014","unstructured":"Yano, M.: A space-time Petrov\u2013Galerkin certified reduced basis method: application to the Boussinesq equations. SIAM J. Sci. Comput. 36(1), A232\u2013A266 (2014)","journal-title":"SIAM J. Sci. Comput."},{"issue":"09","key":"1232_CR58","doi-asserted-by":"publisher","first-page":"1903","DOI":"10.1142\/S0218202514500110","volume":"24","author":"M Yano","year":"2014","unstructured":"Yano, M., Patera, A.T., Urban, K.: A space-time hp-interpolation-based certified reduced basis method for Burgers\u2019 equation. Math. Models Methods Appl. Sci. 24(09), 1903\u20131935 (2014)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"1232_CR59","doi-asserted-by":"crossref","unstructured":"Yilmaz, F., Karas\u00f6zen, B.: An all-at-once approach for the optimal control of the unsteady Burgers equation. J. Comput. Appl. Math. 259, 771\u2013779 (2014). Recent Advances in Applied and Computational Mathematics: ICACM-IAM-METU","DOI":"10.1016\/j.cam.2013.06.036"},{"key":"1232_CR60","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.336","author":"Z Zainib","year":"2020","unstructured":"Zainib, Z., Ballarin, F., Rozza, G., Triverio, P., Jim\u00e9nez-Juan, L., Fremes, S.: Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation. Int. J. Numer. Methods Biomed. Eng. (2020). https:\/\/doi.org\/10.1002\/cnm.336","journal-title":"Int. J. Numer. Methods Biomed. Eng."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01232-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-020-01232-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01232-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T23:31:09Z","timestamp":1622935869000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-020-01232-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6]]},"references-count":60,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["1232"],"URL":"https:\/\/doi.org\/10.1007\/s10915-020-01232-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2020,6]]},"assertion":[{"value":"20 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"55"}}