{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T04:11:21Z","timestamp":1748578281710,"version":"3.41.0"},"reference-count":35,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12161026"],"award-info":[{"award-number":["12161026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The Poisson\u2013Boltzmann equation, which incorporates the source of the Dirac distribution, has been widely applied in predicting the electrostatic potential of biomolecular systems in solution. In this paper we discuss and analyse the virtual element method for the Poisson\u2013Boltzmann equation on general polyhedral meshes. Nearly optimal error estimates, approaching the best possible accuracy, are achieved for the virtual element approximation in both the <jats:italic>L<\/jats:italic>\n                  <jats:sup>2<\/jats:sup>-norm\u202fand <jats:italic>H<\/jats:italic>\n                  <jats:sup>1<\/jats:sup>-norm, even when the solution of the entire domain has low regularity. The efficiency of the virtual element method and the validity of the proposed theoretical prediction are confirmed through numerical experiments conducted on various polyhedral meshes.<\/jats:p>","DOI":"10.1515\/jnma-2023-0085","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T03:21:02Z","timestamp":1740367262000},"page":"187-210","source":"Crossref","is-referenced-by-count":0,"title":["Error analysis of virtual element method for the Poisson\u2013Boltzmann equation"],"prefix":"10.1515","volume":"33","author":[{"given":"Linghan","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Science , Guilin University of Electronic Technology, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Applied Mathematics Center (GUET) , Guilin , 541004 , Guangxi , P.R. China"}]},{"given":"Shi","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education , Xiangtan University , Xiangtan , 411105 , Hunan , P.R. China"}]},{"given":"Ying","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science , Guilin University of Electronic Technology, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guangxi Applied Mathematics Center (GUET) , Guilin , 541004 , Guangxi , P.R. China"}]}],"member":"374","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"2025052922250799916_j_jnma-2023-0085_ref_001","doi-asserted-by":"crossref","unstructured":"F. Fogolari, A. Brigo, and H. 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