{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T21:07:04Z","timestamp":1774386424059,"version":"3.50.1"},"reference-count":28,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100021778","name":"Agencia Nacional de Promoci\u00f3n de la Investigaci\u00f3n, el Desarrollo Tecnol\u00f3gico y la Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PICT 2018-3017"],"award-info":[{"award-number":["PICT 2018-3017"]}],"id":[{"id":"10.13039\/501100021778","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005363","name":"Universidad de Buenos Aires","doi-asserted-by":"publisher","award":["20020170100056BA"],"award-info":[{"award-number":["20020170100056BA"]}],"id":[{"id":"10.13039\/501100005363","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009573","name":"Universidad Nacional de Rosario","doi-asserted-by":"publisher","award":["80020220700222UR"],"award-info":[{"award-number":["80020220700222UR"]}],"id":[{"id":"10.13039\/100009573","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper we study approximations of a singularly perturbed system of two coupled reaction-diffusion equations, in one dimension, by using piecewise linear finite elements on graded meshes. When the parameters are of different magnitudes, the solution exhibits in general two distinct but overlapping boundary layers. We prove that, when the mesh grading parameter is appropriately chosen, optimal error estimates in a balanced norm for piecewise linear elements can be obtained. Supporting numerical results are also presented.<\/jats:p>","DOI":"10.1515\/cmam-2023-0219","type":"journal-article","created":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T12:56:51Z","timestamp":1727787411000},"page":"263-285","source":"Crossref","is-referenced-by-count":1,"title":["A Finite Element Analysis in Balanced Norms for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations"],"prefix":"10.1515","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5855-3711","authenticated-orcid":false,"given":"Mar\u00eda Gabriela","family":"Armentano","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica , Facultad de Ciencias Exactas y Naturales , Universidad de Buenos Aires , Pabell\u00f3n I \u2013 Ciudad Universitaria; and Instituto de Investigaciones Matem\u00e1ticas \u201cLuis A. Santal\u00f3\u201d (IMAS), CONICET \u2013 Universidad de Buenos Aires, Pabell\u00f3n I \u2013 Ciudad Universitaria, 1428 Buenos Aires , Argentina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8608-8263","authenticated-orcid":false,"given":"Ariel L.","family":"Lombardi","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica , Facultad de Ciencias Exactas, Ingenier\u00eda y Agrimensura , 28237 Universidad Nacional de Rosario , Av. Pellegrini 250, S2000BTP Rosario; and CONICET, CCT Rosario , Argentina"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9432-1838","authenticated-orcid":false,"given":"Cecilia","family":"Penessi","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica , Facultad de Ciencias Exactas, Ingenier\u00eda y Agrimensura , 28237 Universidad Nacional de Rosario , Av. Pellegrini 250, S2000BTP Rosario; and CONICET, CCT Rosario , Argentina"}]}],"member":"374","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"2026032417385389924_j_cmam-2023-0219_ref_001","doi-asserted-by":"crossref","unstructured":"J.  Adler, S.  MacLachlan and N.  Madden,\nA first-order system Petrov\u2013Galerkin discretization for a reaction-diffusion problem on a fitted mesh,\nIMA J. Numer. Anal. 36 (2016), no. 3, 1281\u20131309.","DOI":"10.1093\/imanum\/drv045"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_002","doi-asserted-by":"crossref","unstructured":"J. H.  Adler, S.  MacLachlan and N.  Madden,\nFirst-order system least squares finite-elements for singularly perturbed reaction-diffusion equations,\nLarge-Scale Scientific Computing,\nLecture Notes in Comput. Sci. 11958,\nSpringer, Cham (2020), 3\u201314.","DOI":"10.1007\/978-3-030-41032-2_1"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_003","doi-asserted-by":"crossref","unstructured":"M. G.  Armentano, A. L.  Lombardi and C.  Penessi,\nRobust estimates in balanced norms for singularly perturbed reaction diffusion equations using graded meshes,\nJ. Sci. Comput. 96 (2023), no. 1, Paper No. 18.","DOI":"10.1007\/s10915-023-02245-y"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_004","doi-asserted-by":"crossref","unstructured":"J. H.  Bramble, J. E.  Pasciak and O.  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Comp. 71 (2002), no. 237, 147\u2013156.","DOI":"10.1090\/S0025-5718-01-01314-X"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_005","doi-asserted-by":"crossref","unstructured":"Z.  Cai and J.  Ku,\nA dual finite element method for a singularly perturbed reaction-diffusion problem,\nSIAM J. Numer. Anal. 58 (2020), no. 3, 1654\u20131673.","DOI":"10.1137\/19M1264229"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_006","doi-asserted-by":"crossref","unstructured":"P.  Das and J.  Vigo-Aguiar,\nParameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter,\nJ. Comput. Appl. Math. 354 (2019), 533\u2013544.","DOI":"10.1016\/j.cam.2017.11.026"},{"key":"2026032417385389924_j_cmam-2023-0219_ref_007","doi-asserted-by":"crossref","unstructured":"R. G.  Dur\u00e1n and A. L.  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Phys. 35 (1995), no. 4, 429\u2013446."}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0219\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T17:39:04Z","timestamp":1774373944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/cmam-2023-0219\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,2]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,10,2]]},"published-print":{"date-parts":[[2025,4,1]]}},"alternative-id":["10.1515\/cmam-2023-0219"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2023-0219","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,2]]}}}