{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:40:48Z","timestamp":1680266448323},"reference-count":33,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP170100605"],"award-info":[{"award-number":["DP170100605"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology","doi-asserted-by":"publisher","award":["SR\/S4\/MS\/808\/12"],"award-info":[{"award-number":["SR\/S4\/MS\/808\/12"]}],"id":[{"id":"10.13039\/501100001409","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that directly applies to a wide range of numerical schemes, from conforming and non-conforming\nfinite elements, to mixed finite elements, to finite volumes and mimetic finite differences methods.\nOptimal order error estimates for state, adjoint and control variables for low-order schemes are derived under standard regularity assumptions. A novel projection relation between the optimal control and the adjoint variable allows the proof of a super-convergence result for post-processed control. Numerical experiments performed using a modified active set strategy algorithm for conforming, non-conforming and mimetic finite difference methods confirm the theoretical rates of convergence.<\/jats:p>","DOI":"10.1515\/cmam-2017-0054","type":"journal-article","created":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T22:15:51Z","timestamp":1512512151000},"page":"609-637","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Analysis for the Pure Neumann Control Problem Using the Gradient Discretisation Method"],"prefix":"10.1515","volume":"18","author":[{"given":"J\u00e9rome","family":"Droniou","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences , Monash University , Clayton , Victoria 3800 , Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neela","family":"Nataraj","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Indian Institute of Technology Bombay , Powai , Mumbai 400076 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Devika","family":"Shylaja","sequence":"additional","affiliation":[{"name":"Department of Mathematics , IITB-Monash Research Academy , Powai , Mumbai 400076 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,12,5]]},"reference":[{"key":"2023033110390257310_j_cmam-2017-0054_ref_001_w2aab3b7e3097b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Y.  Alnashri and J.  Droniou,\nGradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods,\nComput. Math. Appl. 72 (2016), 2788\u20132807.","DOI":"10.1016\/j.camwa.2016.10.004"},{"key":"2023033110390257310_j_cmam-2017-0054_ref_002_w2aab3b7e3097b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"T.  Apel, J.  Pfefferer and A.  R\u00f6sch,\nFinite element error estimates for Neumann boundary control problems on graded meshes,\nComput. Optim. Appl. 52 (2012), no. 1, 3\u201328.","DOI":"10.1007\/s10589-011-9427-x"},{"key":"2023033110390257310_j_cmam-2017-0054_ref_003_w2aab3b7e3097b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"T.  Apel, J.  Pfefferer and A.  R\u00f6sch,\nFinite element error estimates on the boundary with application to optimal control,\nMath. 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