{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T01:51:25Z","timestamp":1774921885939,"version":"3.50.1"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004410","name":"T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ftirma Kurumu","doi-asserted-by":"publisher","award":["119F022"],"award-info":[{"award-number":["119F022"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s10444-023-10015-5","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T09:02:38Z","timestamp":1677488558000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients"],"prefix":"10.1007","volume":"49","author":[{"given":"Pelin","family":"\u00c7i\u0307lo\u011flu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0313-9767","authenticated-orcid":false,"given":"Hamdullah","family":"Y\u00fccel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"10015_CR1","volume-title":"Verification & Validation in Computational Science and Engineering","author":"PJ Roache","year":"1998","unstructured":"Roache, P.J.: Verification & Validation in Computational Science and Engineering. Hermosa Publishers, Albuquerque (1998)"},{"key":"10015_CR2","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s00791-010-0134-4","volume":"13","author":"A Borz\u00ec","year":"2010","unstructured":"Borz\u00ec, A.: Multigrid and sparse-grid schemes for elliptic control problems with random coefficients. Comput. Vis. Sci. 13, 153\u2013160 (2010)","journal-title":"Comput. Vis. Sci."},{"issue":"2","key":"10015_CR3","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1002\/gamm.201010017","volume":"33","author":"A Borz\u00ec","year":"2010","unstructured":"Borz\u00ec, A., Schulz, V., Schillings, C., von Winckel, G.: On the treatment of distributed uncertainties in PDE constrained optimization. GAMM Mitteilungen 33(2), 230\u2013246 (2010)","journal-title":"GAMM Mitteilungen"},{"issue":"4","key":"10015_CR4","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."},{"key":"10015_CR5","doi-asserted-by":"publisher","first-page":"466","DOI":"10.1137\/16M109870X","volume":"5","author":"AA Ali","year":"2017","unstructured":"Ali, A.A., Ullmann, E., Hinze, M.: Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients. SIAM\/ASA J. Uncertain. Quantif. 5, 466\u2013492 (2017)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"10015_CR6","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1016\/j.crma.2014.04.007","volume":"352","author":"M Lazar","year":"2014","unstructured":"Lazar, M., Zuazua, E.: Averaged control and observation of parameter-depending wave equations. C. R. Math. Acad. Sci. Paris 352, 497\u2013502 (2014)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"issue":"12","key":"10015_CR7","doi-asserted-by":"publisher","first-page":"3077","DOI":"10.1016\/j.automatica.2014.10.054","volume":"50","author":"E Zuazua","year":"2014","unstructured":"Zuazua, E.: Averaged control. Automatica 50(12), 3077\u20133087 (2014)","journal-title":"Automatica"},{"key":"10015_CR8","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1137\/16M1057607","volume":"39","author":"S Garreis","year":"2017","unstructured":"Garreis, S., Ulbrich, M.: Constrained optimization with low-rank tensors and applications to parametric problems with PDEs. SIAM J. Sci. Comput. 39, 25\u201354 (2017)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"10015_CR9","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.1137\/100801731","volume":"49","author":"MD Gunzburger","year":"2011","unstructured":"Gunzburger, M.D., Lee, H.-C., Lee, J.: Error estimates of stochastic optimal Neumann boundary control problems. SIAM J. Numer. Anal. 49(4), 1532\u20131552 (2011)","journal-title":"SIAM J. Numer. Anal."},{"key":"10015_CR10","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jmaa.2010.07.036","volume":"384","author":"LS Hou","year":"2011","unstructured":"Hou, L.S., Lee, J., Manouzi, H.: Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs. J. Math. Anal. Appl. 384, 87\u2013103 (2011)","journal-title":"J. Math. Anal. Appl."},{"key":"10015_CR11","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1137\/120892362","volume":"35","author":"DP Kouri","year":"2013","unstructured":"Kouri, D.P., Heinkenschloss, M., Ridzal, D., van Bloemen Waanders, B.G.: A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty. SIAM J. Sci. Comput. 35, 1847\u20131879 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR12","first-page":"77","volume":"14","author":"H-C Lee","year":"2013","unstructured":"Lee, H.-C., Lee, J.: A stochastic Galerkin method for stochastic control problems. Commun. Comput. Phys. 14, 77\u2013106 (2013)","journal-title":"Commun. Comput. Phys."},{"key":"10015_CR13","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/j.cma.2011.11.026","volume":"213\/216","author":"E Rosseel","year":"2012","unstructured":"Rosseel, E., Wells, G.N.: Optimal control with stochastic PDE constraints and uncertain controls. Comput. Methods Appl. Mech. Engrg. 213\/216, 152\u2013167 (2012)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"10015_CR14","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1137\/15M1018502","volume":"37","author":"P Benner","year":"2016","unstructured":"Benner, P., Onwunta, A., Stoll, M.: Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. SIAM J. Matrix Anal. Appl. 37, 491\u2013518 (2016)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10015_CR15","doi-asserted-by":"publisher","first-page":"2700","DOI":"10.1137\/120884158","volume":"51","author":"P Chen","year":"2013","unstructured":"Chen, P., Quarteroni, A., Rozza, G.: Stochastic optimal Robin boundary control problems of advection-dominated elliptic equations. SIAM J. Numer. Anal. 51, 2700\u20132722 (2013)","journal-title":"SIAM J. Numer. Anal."},{"key":"10015_CR16","doi-asserted-by":"publisher","first-page":"1034","DOI":"10.1137\/15M1041390","volume":"4","author":"A Kunoth","year":"2016","unstructured":"Kunoth, A., Schwab, C.: Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems. SIAM\/ASA J. Uncertain. Quantif. 4, 1034\u20131059 (2016)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"issue":"5","key":"10015_CR17","doi-asserted-by":"publisher","first-page":"2659","DOI":"10.1137\/110835438","volume":"50","author":"H Tiesler","year":"2012","unstructured":"Tiesler, H., Kirby, R.M., Xiu, D., Preusser, T.: Stochastic collocation for optimal control problems with stochastic PDE constraints. SIAM J. Control Optim. 50(5), 2659\u20132682 (2012)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"10015_CR18","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1137\/19M1294952","volume":"9","author":"PA Guth","year":"2021","unstructured":"Guth, P.A., Kaarnioja, V., Kuo, F.Y., Schillings, C., Sloan, I.H.: A quasi-Monte Carlo method for optimal control under uncertainty. SIAM\/ASA J. Uncertain. Quantif. 9(2), 354\u2013383 (2021)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"issue":"1","key":"10015_CR19","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1137\/17M1155892","volume":"7","author":"AV Barel","year":"2019","unstructured":"Barel, A.V., Vandewalle, S.: Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method. SIAM\/ASA J. Uncertain. Quantif. 7(1), 174\u2013202 (2019)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"issue":"3","key":"10015_CR20","doi-asserted-by":"publisher","first-page":"2172","DOI":"10.1137\/070711311","volume":"31","author":"A Borz\u00ec","year":"2009","unstructured":"Borz\u00ec, A., von Winckel, G.: Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients. SIAM J. Sci. Comput. 31(3), 2172\u20132192 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR21","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1080\/01630563.2018.1508034","volume":"40","author":"L Ge","year":"2019","unstructured":"Ge, L., Sun, T.: A sparse grid stochastic collocation discontinuous Galerkin method for constrained optimal control problem governed by random convection dominated diffusion equations. Numer. Func. Anal. Optim. 40, 763\u2013797 (2019)","journal-title":"Numer. Func. Anal. Optim."},{"key":"10015_CR22","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s10915-015-0091-7","volume":"67","author":"T Sun","year":"2016","unstructured":"Sun, T., Shen, W., Gong, B., Liu, W.: A priori error estimate of stochastic Galerkin method for optimal control problem governed by stochastic elliptic PDE with constrained control. J. Sci. Comput. 67, 405\u2013431 (2016)","journal-title":"J. Sci. Comput."},{"key":"10015_CR23","doi-asserted-by":"publisher","first-page":"112602","DOI":"10.1016\/j.cam.2019.112602","volume":"370","author":"J D\u00fcrrw\u00e4chter","year":"2020","unstructured":"D\u00fcrrw\u00e4chter, J., Kuhn, T., Meyer, F., Schlachter, L., Schneider, F.: A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations. J. Comput. Appl. Math. 370, 112602 (2020)","journal-title":"J. Comput. Appl. Math."},{"key":"10015_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2553-7","volume-title":"Monte Carlo: Concepts, Algorithms, and Applications","author":"GS Fishman","year":"1996","unstructured":"Fishman, G.S.: Monte Carlo: Concepts, Algorithms, and Applications. Springer, New York (1996)"},{"key":"10015_CR25","volume-title":"Monte Carlo Strategies in Scientific Computing. Springer Series in Statistics","author":"JS Liu","year":"2008","unstructured":"Liu, J.S.: Monte Carlo Strategies in Scientific Computing. Springer Series in Statistics. Springer, New York (2008)"},{"issue":"2","key":"10015_CR26","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1137\/S1064827501387826","volume":"24","author":"D Xiu","year":"2002","unstructured":"Xiu, D., Karniadakis, G.E.: The Wiener\u2013Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619\u2013644 (2002)","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"10015_CR27","doi-asserted-by":"publisher","first-page":"2443","DOI":"10.1016\/j.jcp.2008.12.018","volume":"228","author":"G Po\u00ebtte","year":"2009","unstructured":"Po\u00ebtte, G., Despr\u00e9s, B., Lucor, D.: Uncertainty quantification for systems of conservation laws. J. Comput. Phys. 228(7), 2443\u20132467 (2009)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"10015_CR28","doi-asserted-by":"publisher","first-page":"2215","DOI":"10.1051\/m2an\/2018072","volume":"52","author":"P \u00d6ffner","year":"2018","unstructured":"\u00d6ffner, P., Glaubitz, J., Ranocha, H.: Stability of correction procedure via reconstruction with summation-by-parts operators for Burgers\u2019 equation using a polynomial chaos approach. ESAIM: M2AN 52(6), 2215\u20132245 (2018)","journal-title":"ESAIM: M2AN"},{"issue":"4","key":"10015_CR29","doi-asserted-by":"publisher","first-page":"2012","DOI":"10.1137\/110826953","volume":"50","author":"D Leykekhman","year":"2012","unstructured":"Leykekhman, D., Heinkenschloss, M.: Local error analysis of discontinuous Galerkin methods for advection-dominated elliptic linear-quadratic optimal control problems. SIAM J. Numer. Anal. 50(4), 2012\u20132038 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"10015_CR30","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/s10589-014-9691-7","volume":"62","author":"H Y\u00fccel","year":"2015","unstructured":"Y\u00fccel, H., Benner, P.: Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations. Comput. Optim. Appl. 62, 291\u2013321 (2015)","journal-title":"Comput. Optim. Appl."},{"key":"10015_CR31","doi-asserted-by":"crossref","unstructured":"Y\u00fccel, H., Heinkenschloss, M., Karas\u00f6zen, B.: Distributed Optimal Control of Diffusion-Convection-Reaction Equations Using Discontinuous Galerkin Methods. In: Numer. Math. Adv. Appl. 2011, pp 389\u2013397. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-33134-3_42"},{"issue":"5","key":"10015_CR32","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"DN Arnold","year":"2002","unstructured":"Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749\u20131779 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"10015_CR33","doi-asserted-by":"crossref","unstructured":"Rivi\u00e8re, B.: Discontinuous galerkin methods for solving elliptic and parabolic equations. Theory and implementation. Frontiers Appl. Math SIAM (2008)","DOI":"10.1137\/1.9780898717440"},{"key":"10015_CR34","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp. 7, 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"10015_CR35","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1002\/nla.1818","volume":"20","author":"J Ballani","year":"2013","unstructured":"Ballani, J., Grasedyck, L.: A projection method to solve linear systems in tensor product. Numer. Linear Algebra Appl. 20, 27\u201343 (2013)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"4","key":"10015_CR36","doi-asserted-by":"publisher","first-page":"1288","DOI":"10.1137\/100799010","volume":"32","author":"D Kressner","year":"2011","unstructured":"Kressner, D., Tobler, C.: Low-rank tensor Krylov subspace methods for parametrized linear systems. SIAM J. Matrix Anal. Appl. 32(4), 1288\u20131316 (2011)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"10015_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/130926365","volume":"37","author":"M Stoll","year":"2015","unstructured":"Stoll, M., Breiten, T.: A low-rank in time approach to PDE-constrained optimization. SIAM J. Sci. Comput. 37(1), 1\u201329 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR38","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.cma.2016.02.004","volume":"304","author":"P Benner","year":"2016","unstructured":"Benner, P., Dolgov, S., Onwunta, A., Stoll, M.: Low\u2013rank solvers for unsteady Stokes\u2013Brinkman optimal control problem with random data. Comput. Methods Appl. Mech. Engrg. 304, 26\u201354 (2016)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"11","key":"10015_CR39","first-page":"1653","volume":"91","author":"P Benner","year":"2020","unstructured":"Benner, P., Dolgov, S., Onwunta, A., Stoll, M.: Low-rank solution of an optimal control problem constrained by random Navier\u2013Stokes equations. SIAM J. Sci. Comput. 91(11), 1653\u20131678 (2020)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR40","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1137\/16M1057607","volume":"39","author":"S Garreis","year":"2017","unstructured":"Garreis, S., Ulbrich, M.: Constrained optimization with low-rank tensors and applications to parametric problems with PDEs. SIAM J. Sci. Comput. 39, 25\u201354 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65024-6","volume-title":"Optimal Control of Systems Governed by Partial Differential Equations","author":"J-L Lions","year":"1971","unstructured":"Lions, J.-L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer, Berlin (1971)"},{"key":"10015_CR42","doi-asserted-by":"crossref","unstructured":"Tr\u00f6ltzsch, F.: Optimal Control of Partial Differential Equations: theory, Methods and Applications. Graduate Studies in Mathematics, vol. 112 American Mathematical Society (2010)","DOI":"10.1090\/gsm\/112"},{"issue":"2","key":"10015_CR43","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1137\/S0036142902418680","volume":"42","author":"I Babu\u0161ka","year":"2004","unstructured":"Babu\u0161ka, I., Tempone, R., Zouraris, G.E.: Galerkin finite element approximations of stochastic elliptic partial differential equations. SIAM J. Numer. Anal. 42(2), 800\u2013825 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"10015_CR44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139017329","volume-title":"An Introduction to Computational Stochastic PDEs","author":"GJ Lord","year":"2014","unstructured":"Lord, G.J., Powell, C.E., Shardlow, T.: An Introduction to Computational Stochastic PDEs. Cambridge University Press, New York (2014)"},{"key":"10015_CR45","doi-asserted-by":"publisher","first-page":"897","DOI":"10.2307\/2371268","volume":"60","author":"N Wiener","year":"1938","unstructured":"Wiener, N.: The homogeneous chaos. Amer. J. Math. 60, 897\u2013938 (1938)","journal-title":"Amer. J. Math."},{"issue":"37","key":"10015_CR46","first-page":"79","volume":"1947","author":"K Karhunen","year":"1947","unstructured":"Karhunen, K.: \u00dcBer lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys. 1947(37), 79 (1947)","journal-title":"Ann. Acad. Sci. Fennicae. Ser. A. I. Math.-Phys."},{"key":"10015_CR47","first-page":"195","volume":"84","author":"M Lo\u00e8ve","year":"1946","unstructured":"Lo\u00e8ve, M.: Fonctions al\u00e9atoires de second ordre. Revue Sci. 84, 195\u2013206 (1946)","journal-title":"Revue Sci."},{"issue":"37-38","key":"10015_CR48","doi-asserted-by":"publisher","first-page":"4093","DOI":"10.1016\/S0045-7825(02)00354-7","volume":"191","author":"I Babu\u0161ka","year":"2002","unstructured":"Babu\u0161ka, I., Chatzipantelidis, P.: On solving elliptic stochastic partial differential equations. Comput. Methods Appl. Mech. Engrg. 191(37-38), 4093\u20134122 (2002)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"2","key":"10015_CR49","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1093\/imanum\/drn014","volume":"29","author":"CE Powell","year":"2009","unstructured":"Powell, C.E., Elman, H.C.: Block\u2013diagonal preconditioning for spectral stochastic finite\u2013element systems. IMA J. Numer. Anal. 29(2), 350\u2013375 (2009)","journal-title":"IMA J. Numer. Anal."},{"key":"10015_CR50","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14394-6","volume-title":"Stochastic Differential Equations","author":"B \u00d8ksendal","year":"2003","unstructured":"\u00d8ksendal, B.: Stochastic Differential Equations. Springer, Berlin (2003)"},{"key":"10015_CR51","doi-asserted-by":"publisher","first-page":"385","DOI":"10.2307\/1969178","volume":"48","author":"RH Cameron","year":"1947","unstructured":"Cameron, R.H., Martin, W.T.: The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals. Ann. of Math. (2) 48, 385\u2013392 (1947)","journal-title":"Ann. of Math. (2)"},{"key":"10015_CR52","doi-asserted-by":"publisher","first-page":"1848","DOI":"10.1137\/080742282","volume":"31","author":"OG Ernst","year":"2010","unstructured":"Ernst, O.G., Ullmann, E.: Stochastic Galerkin matrices. SIAM J. Matrix Anal. Appl. 31, 1848\u20131872 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"10015_CR53","doi-asserted-by":"publisher","first-page":"1545","DOI":"10.1051\/m2an\/2022054","volume":"56","author":"A Barth","year":"2022","unstructured":"Barth, A., Stein, A.: Numerical analysis for time-dependent advection diffusion problems with random discontinuous coefficients. ESAIM: M2AN 56(5), 1545\u20131578 (2022)","journal-title":"ESAIM: M2AN"},{"key":"10015_CR54","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.apnum.2021.10.007","volume":"172","author":"P \u00c7i\u0307lo\u011flu","year":"2022","unstructured":"\u00c7i\u0307lo\u011flu, P., Y\u00fccel, H.: Stochastic discontinuous Galerkin methods with low\u2013rank solvers for convection diffusion equations. Appl. Numer. Math 172, 157\u2013185 (2022)","journal-title":"Appl. Numer. Math"},{"issue":"5","key":"10015_CR55","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1137\/S0363012901389342","volume":"41","author":"R Li","year":"2002","unstructured":"Li, R., Liu, W., Ma, H., Tang, T.: Adaptive finite element approximation for distributed elliptic optimal control problems. SIAM J. Control Optim. 41(5), 1321\u20131349 (2002)","journal-title":"SIAM J. Control Optim."},{"key":"10015_CR56","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1007\/s10589-013-9601-4","volume":"57","author":"T Akman","year":"2014","unstructured":"Akman, T., Y\u00fccel, H., Karas\u00f6zen, B.: A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations. Comput. Optim. Appl. 57, 703\u2013729 (2014)","journal-title":"Comput. Optim. Appl."},{"issue":"3","key":"10015_CR57","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1137\/070694016","volume":"47","author":"D Meidner","year":"2008","unstructured":"Meidner, D., Vexler, B.: A priori error estimates for space-time finite element discretization of parabolic optimal control problems. I. Problems without control constraints. SIAM J. Control Optim. 47(3), 1150\u20131177 (2008)","journal-title":"SIAM J. Control Optim."},{"issue":"4","key":"10015_CR58","first-page":"681","volume":"7","author":"Z Zhou","year":"2010","unstructured":"Zhou, Z., Yan, N.: The local discontinuous Galerkin method for optimal control problem governed by convection diffusion equations. Int. J. Numer. Anal. Model. 7(4), 681\u2013699 (2010)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"10015_CR59","volume-title":"Sobolev Spaces","author":"RA Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. Academic Press, Orlando (1975)"},{"issue":"4","key":"10015_CR60","doi-asserted-by":"publisher","first-page":"1176","DOI":"10.1137\/S0363012997328609","volume":"37","author":"M Bergounioux","year":"1999","unstructured":"Bergounioux, M., Ito, K., Kunisch, K.: Primal-dual strategy for constrained optimal control problems. SIAM J. Control Optim. 37(4), 1176\u20131194 (1999)","journal-title":"SIAM J. Control Optim."},{"issue":"3","key":"10015_CR61","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1007\/s00211-013-0521-0","volume":"124","author":"P Benner","year":"2013","unstructured":"Benner, P., Breiten, T.: Low rank methods for a class of generalized Lyapunov equations and related issues. Numer. Math. 124(3), 441\u2013470 (2013)","journal-title":"Numer. Math."},{"key":"10015_CR62","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.jcp.2017.12.039","volume":"357","author":"MA Freitag","year":"2018","unstructured":"Freitag, M.A., Green, D.L.H.: A low\u2013rank approach to the solution of weak constraint variational data assimilation problems. J. Comput. Phys. 357, 263\u2013281 (2018)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10015_CR63","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1137\/16M1075582","volume":"39","author":"K Lee","year":"2017","unstructured":"Lee, K., Elman, H.C.: A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations. SIAM J. Sci. Comput. 39(5), 828\u2013850 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR64","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1137\/130937251","volume":"3","author":"P Benner","year":"2015","unstructured":"Benner, P., Onwunta, A., Stoll, M.: Low-rank solution of unsteady diffusion equations with stochastic coefficients. SIAM\/ASA J. Uncertain. Quantif. 3, 622\u2013649 (2015)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"issue":"5","key":"10015_CR65","doi-asserted-by":"publisher","first-page":"2641","DOI":"10.1137\/100817279","volume":"33","author":"M Gunzburger","year":"2011","unstructured":"Gunzburger, M., Ming, J.: Optimal control of stochastic flow over a backward-facing step using reduced-order modeling. SIAM J. Sci. Comput. 33(5), 2641\u20132663 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"10015_CR66","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1137\/130940517","volume":"2","author":"P Chen","year":"2014","unstructured":"Chen, P., Quarteroni, A.: Weighted reduced basis method for stochastic optimal control problems with elliptic PDE constraint. SIAM\/ASA J. Uncertain. Quantif. 2, 364\u2013396 (2014)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-023-10015-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-023-10015-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-023-10015-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T16:18:48Z","timestamp":1682007528000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-023-10015-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,27]]},"references-count":66,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10015"],"URL":"https:\/\/doi.org\/10.1007\/s10444-023-10015-5","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,27]]},"assertion":[{"value":"15 April 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}],"article-number":"16"}}