{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:32:56Z","timestamp":1772303576371,"version":"3.50.1"},"reference-count":35,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology, India","doi-asserted-by":"publisher","award":["CRG\/2020\/001599"],"award-info":[{"award-number":["CRG\/2020\/001599"]}],"id":[{"id":"10.13039\/501100001409","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research, India","doi-asserted-by":"publisher","award":["1044\/(CSIR-UGC NET DEC.2018)"],"award-info":[{"award-number":["1044\/(CSIR-UGC NET DEC.2018)"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler\u2019s scheme for temporal discretization.\nWith the help of Ritz\u2013Voltera and <jats:inline-formula>\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>L<\/m:mi>\n                              <m:mn>2<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2023-0061_ineq_0001.png\"\/>\n                        <jats:tex-math>L^{2}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> projection operators, optimal a priori error estimates are established.\nMoreover, several numerical experiments are presented to confirm the computational efficiency of the proposed scheme and validate the theoretical findings.<\/jats:p>","DOI":"10.1515\/cmam-2023-0061","type":"journal-article","created":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T00:00:45Z","timestamp":1696982445000},"page":"1001-1019","source":"Crossref","is-referenced-by-count":6,"title":["A Conforming Virtual Element Method for Parabolic Integro-Differential Equations"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4195-2740","authenticated-orcid":false,"given":"Sangita","family":"Yadav","sequence":"first","affiliation":[{"name":"Department of Mathematics , Birla Institute of Technology and Science , Pilani , Pilani Campus , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meghana","family":"Suthar","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Birla Institute of Technology and Science , Pilani , Pilani Campus , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sarvesh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Indian Institute of Space Science and Technology , Thiruvananthapuram , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,10,11]]},"reference":[{"key":"2024100217254205951_j_cmam-2023-0061_ref_001","doi-asserted-by":"crossref","unstructured":"H. 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Marini and A. Russo,\nVirtual element method for general second-order elliptic problems on polygonal meshes,\nMath. Models Methods Appl. Sci. 26 (2016), no. 4, 729\u2013750.","DOI":"10.1142\/S0218202516500160"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_005","doi-asserted-by":"crossref","unstructured":"J. R. Cannon and Y. P. Lin,\nA priori \n                  \n                     \n                        \n                           L\n                           2\n                        \n                     \n                     \n                     L^{2}\n                  \n                error estimates for finite-element methods for nonlinear diffusion equations with memory,\nSIAM J. Numer. Anal. 27 (1990), no. 3, 595\u2013607.","DOI":"10.1137\/0727036"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_006","doi-asserted-by":"crossref","unstructured":"M. Dehghan and Z. Gharibi,\nVirtual element method for solving an inhomogeneous Brusselator model with and without cross-diffusion in pattern formation,\nJ. Sci. Comput. 89 (2021), no. 1, Paper No. 16.","DOI":"10.1007\/s10915-021-01626-5"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_007","doi-asserted-by":"crossref","unstructured":"M. Dehghan and Z. Gharibi,\nA unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineering,\nComput. Math. Appl. 121 (2022), 30\u201351.","DOI":"10.1016\/j.camwa.2022.06.004"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_008","doi-asserted-by":"crossref","unstructured":"M. Dehghan, Z. Gharibi and M. R. Eslahchi,\nUnconditionally energy stable \n                  \n                     \n                        \n                           C\n                           0\n                        \n                     \n                     \n                     C^{0}\n                  \n               -virtual element scheme for solving generalized Swift\u2013Hohenberg equation,\nAppl. Numer. Math. 178 (2022), 304\u2013328.","DOI":"10.1016\/j.apnum.2022.03.013"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_009","doi-asserted-by":"crossref","unstructured":"M. Dehghan, Z. Gharibi and R. Ruiz-Baier,\nOptimal error estimates of coupled and divergence-free virtual element methods for the Poisson\u2013Nernst\u2013Planck\/Navier\u2013Stokes equations and applications in electrochemical systems,\nJ. Sci. Comput. 94 (2023), no. 3, Paper No. 72.","DOI":"10.1007\/s10915-023-02126-4"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_010","doi-asserted-by":"crossref","unstructured":"M. Dehghan and F. Shakeri,\nSolution of parabolic integro-differential equations arising in heat conduction in materials with memory via He\u2019s variational iteration technique,\nInt. J. Numer. Methods Biomed. Eng. 26 (2010), no. 6, 705\u2013715.","DOI":"10.1002\/cnm.1166"},{"key":"2024100217254205951_j_cmam-2023-0061_ref_011","doi-asserted-by":"crossref","unstructured":"B. Deka and R. C. 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Comp. 60 (1993), no. 201, 133\u2013166.","DOI":"10.1090\/S0025-5718-1993-1149295-4"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0061\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0061\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T17:26:52Z","timestamp":1727890012000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0061\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,11]]},"references-count":35,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,1,2]]},"published-print":{"date-parts":[[2024,10,1]]}},"alternative-id":["10.1515\/cmam-2023-0061"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2023-0061","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,11]]}}}