{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T21:55:55Z","timestamp":1775858155149,"version":"3.50.1"},"reference-count":52,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["SRG\/2020\/001027"],"award-info":[{"award-number":["SRG\/2020\/001027"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["SPF\/2020\/000019"],"award-info":[{"award-number":["SPF\/2020\/000019"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This article discusses the quasi-optimality of adaptive nonconforming finite element methods for distributed optimal control problems governed by \ud835\udc5a-harmonic operators for <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>m<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:mrow>\n                                 <m:mn>1<\/m:mn>\n                                 <m:mo>,<\/m:mo>\n                                 <m:mn>2<\/m:mn>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2023-0083_ineq_0001.png\"\/>\n                        <jats:tex-math>m=1,2<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nA variational discretization approach is employed and the state and adjoint variables are discretized using nonconforming finite elements.\nError equivalence results at the continuous and discrete levels lead to a priori and a posteriori error estimates for the optimal control problem.\nThe general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality.\nNumerical results demonstrate the theoretically predicted orders of convergence and the efficiency of the adaptive estimator.<\/jats:p>","DOI":"10.1515\/cmam-2023-0083","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T10:23:53Z","timestamp":1707474233000},"page":"599-622","source":"Crossref","is-referenced-by-count":3,"title":["Convergence of Adaptive Crouzeix\u2013Raviart and Morley FEM for Distributed Optimal Control Problems"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1663-334X","authenticated-orcid":false,"given":"Asha K.","family":"Dond","sequence":"first","affiliation":[{"name":"School of Mathematics , 193159 Indian Institute of Science Education and Research Thiruvananthapuram , Thiruvananthapuram 695551 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neela","family":"Nataraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics , 29491 Indian Institute of Technology Bombay , Powai , Mumbai 400076; and School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram 695551 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Subham","family":"Nayak","sequence":"additional","affiliation":[{"name":"School of Mathematics , 193159 Indian Institute of Science Education and Research Thiruvananthapuram , Thiruvananthapuram 695551 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,2,10]]},"reference":[{"key":"2024070116105006183_j_cmam-2023-0083_ref_001","doi-asserted-by":"crossref","unstructured":"R. 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