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To overcome this drawback, first of all, we propose a POD-DEIM technique with a correction term that includes missing information in the reduced models. To improve the computational efficiency, we propose an adaptive version of this algorithm in time that accounts for the peculiar dynamics of the RD-PDE in presence of Turing instability. We show the effectiveness of the proposed methods in terms of accuracy and computational cost for a selection of RD systems, i.e., FitzHugh\u2013Nagumo, Schnakenberg and the morphochemical DIB models, with increasing degree of nonlinearity and more structured patterns.<\/jats:p>","DOI":"10.1515\/jnma-2022-0025","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T09:29:01Z","timestamp":1674120541000},"page":"205-229","source":"Crossref","is-referenced-by-count":8,"title":["Adaptive POD-DEIM correction for Turing pattern approximation in reaction\u2013diffusion PDE systems"],"prefix":"10.1515","volume":"31","author":[{"given":"Alessandro","family":"Alla","sequence":"first","affiliation":[{"name":"Universit\u00e0 Ca' Foscari Venezia, Dipartimento di Scienze Molecolari e Nanosistemi , Venezia , Italy"}]},{"given":"Angela","family":"Monti","sequence":"additional","affiliation":[{"name":"Universit\u00e0 del Salento, Dipartimento di Matematica e Fisica \u2018E. De Giorgi\u2019 , Lecce , Italy"}]},{"given":"Ivonne","family":"Sgura","sequence":"additional","affiliation":[{"name":"Universit\u00e0 del Salento, Dipartimento di Matematica e Fisica \u2018E. De Giorgi\u2019 , Lecce , Italy"}]}],"member":"374","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"2023090804423799225_j_jnma-2022-0025_ref_001","doi-asserted-by":"crossref","unstructured":"A. Alla and M. Falcone, A time-adaptive POD method for optimal control problems, IFAC Proc. Volumes 46 (2013), No. 26, 245\u2013250.","DOI":"10.3182\/20130925-3-FR-4043.00042"},{"key":"2023090804423799225_j_jnma-2022-0025_ref_002","doi-asserted-by":"crossref","unstructured":"A. Alla and J. N. Kutz, Randomized model order reduction, Adv. Comput. Math. 45 (2019), 1251\u20131271.","DOI":"10.1007\/s10444-018-09655-9"},{"key":"2023090804423799225_j_jnma-2022-0025_ref_003","doi-asserted-by":"crossref","unstructured":"D. Amsallem and C. 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