{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T12:29:47Z","timestamp":1778588987188,"version":"3.51.4"},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["17K17948"],"award-info":[{"award-number":["17K17948"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18K03434"],"award-info":[{"award-number":["18K03434"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["20K03752"],"award-info":[{"award-number":["20K03752"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this study, we present new sharper constructive a priori error estimates for a full-discrete numerical solution of the heat equation that refines our previous work. The full discretization is given using the finite element method in space and linear interpolation in time, similar to that in the previous work. In particular, we adopt an approach based on the effective use of the properties both for exact and discretized time-periodic solutions to establish the error estimates simpler and sharper than the previous work. Furthermore, we derive some time-stepwise error estimates in the space direction. Finally, we present several numerical examples that confirm the actual refinements of the convergence.<\/jats:p>","DOI":"10.1515\/cmam-2022-0015","type":"journal-article","created":{"date-parts":[[2022,5,26]],"date-time":"2022-05-26T11:23:51Z","timestamp":1653564231000},"page":"631-647","source":"Crossref","is-referenced-by-count":2,"title":["Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation"],"prefix":"10.1515","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4147-1864","authenticated-orcid":false,"given":"Takuma","family":"Kimura","sequence":"first","affiliation":[{"name":"Department of Information Science , Saga University , Saga 840-8502 , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6081-2324","authenticated-orcid":false,"given":"Teruya","family":"Minamoto","sequence":"additional","affiliation":[{"name":"Department of Information Science , Saga University , Saga 840-8502 , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5228-0591","authenticated-orcid":false,"given":"Mitsuhiro T.","family":"Nakao","sequence":"additional","affiliation":[{"name":"Faculty of Science and Engineering , Waseda University , Tokyo 169-8555 , Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,5,26]]},"reference":[{"key":"2023033112440962635_j_cmam-2022-0015_ref_001","doi-asserted-by":"crossref","unstructured":"V.  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Nakao,\nConstructive error estimates for full discrete approximation of periodic solution for heat equation,\nJ. Comput. Appl. Math. 368 (2020), Article ID 112510.","DOI":"10.1016\/j.cam.2019.112510"},{"key":"2023033112440962635_j_cmam-2022-0015_ref_005","doi-asserted-by":"crossref","unstructured":"M.  Mizuguchi, M. T.  Nakao, K.  Sekine and S.  Oishi,\nError constants for the semi-discrete Galerkin approximation of the linear heat equation,\nJ. Sci. Comput. 89 (2021), 10.1007\/s10915-021-01636-3.","DOI":"10.1007\/s10915-021-01636-3"},{"key":"2023033112440962635_j_cmam-2022-0015_ref_006","doi-asserted-by":"crossref","unstructured":"M. T.  Nakao,\nSolving nonlinear parabolic problenis with result verification. Part I: One-space-dimensional case,\nJ. Comput. Appl. Math. 38 (1991), 323\u2013334.","DOI":"10.1016\/0377-0427(91)90179-N"},{"key":"2023033112440962635_j_cmam-2022-0015_ref_007","doi-asserted-by":"crossref","unstructured":"M. T.  Nakao, T.  Kimura and T.  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