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Concerning the parabolic case, a stabilized space-time framework will be considered and stabilization will also occur in both bilinear forms involving time derivatives. Then we will build Reduced Order Models on this discretization procedure and two possible settings can be analyzed: whether or not stabilization is needed in the online phase, too. In order to build the reduced bases for state, control, and adjoint variables we will consider a Proper Orthogonal Decomposition algorithm in a partitioned approach. It is the first time that Reduced Order Models are applied to stabilized parabolic problems in this setting.\nThe discussion is supported by computational experiments, where relative errors between the FEM and ROM solutions are studied together with the respective computational times.<\/jats:p>","DOI":"10.1515\/cmam-2023-0171","type":"journal-article","created":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T18:07:54Z","timestamp":1713895674000},"page":"237-260","source":"Crossref","is-referenced-by-count":6,"title":["A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control"],"prefix":"10.1515","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5845-8415","authenticated-orcid":false,"given":"Fabio","family":"Zoccolan","sequence":"first","affiliation":[{"name":"Institute of Mathematics , 27218 \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , 1015 Lausanne , Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1245-271X","authenticated-orcid":false,"given":"Maria","family":"Strazzullo","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences \u201dGiuseppe Luigi Lagrange\u201d , 19032 Politecnico di Torino , Corso Duca degli Abruzzi 24, 10129 , Turin , Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0810-8812","authenticated-orcid":false,"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[{"name":"mathLab , Mathematics Area , 19040 SISSA , via Bonomea 265, 34136 Trieste , Italy"}]}],"member":"374","published-online":{"date-parts":[[2024,4,24]]},"reference":[{"key":"2025010318340301771_j_cmam-2023-0171_ref_001","unstructured":"T.  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