{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:10:44Z","timestamp":1776802244513,"version":"3.51.2"},"reference-count":34,"publisher":"American Mathematical Society (AMS)","issue":"305","license":[{"start":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T00:00:00Z","timestamp":1497916800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001502","name":"Department of Atomic Energy, Government of India","doi-asserted-by":"publisher","award":["DAE File No: 2\/39(6)\/2010\/NBHM\/R&amp;D-II"],"award-info":[{"award-number":["DAE File No: 2\/39(6)\/2010\/NBHM\/R&amp;D-II"]}],"id":[{"id":"10.13039\/501100001502","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this article, an alternative energy-space based approach is proposed for the Dirichlet boundary control problem and then a finite-element based numerical method is designed and analyzed for its numerical approximation. A priori error estimates of optimal order in the energy norm and the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L 2\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">L_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm are derived. Moreover, a reliable and efficient a posteriori error estimator is derived with the help of an auxiliary problem. The theoretical results are illustrated by the numerical experiments.\n                  <\/p>","DOI":"10.1090\/mcom\/3125","type":"journal-article","created":{"date-parts":[[2015,10,30]],"date-time":"2015-10-30T11:11:10Z","timestamp":1446203470000},"page":"1103-1126","source":"Crossref","is-referenced-by-count":39,"title":["Error bounds for a Dirichlet boundary control problem based on energy spaces"],"prefix":"10.1090","volume":"86","author":[{"given":"Sudipto","family":"Chowdhury","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thirupathi","family":"Gudi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Nandakumaran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2016,6,20]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10589-011-9427-x","article-title":"Finite element error estimates for Neumann boundary control problems on graded meshes","volume":"52","author":"Apel, Thomas","year":"2012","journal-title":"Comput. 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