{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T12:20:15Z","timestamp":1783081215796,"version":"3.54.6"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,12,1]],"date-time":"2026-12-01T00:00:00Z","timestamp":1796083200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of Hunan Province","doi-asserted-by":"publisher","award":["2025JJ50035"],"award-info":[{"award-number":["2025JJ50035"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019081","name":"Science and Technology Program of Hunan Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100019081","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005374","name":"Nanjing University of Posts and Telecommunications","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100005374","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12501543"],"award-info":[{"award-number":["12501543"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12571388"],"award-info":[{"award-number":["12571388"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,12]]},"DOI":"10.1016\/j.cam.2026.117734","type":"journal-article","created":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T07:02:53Z","timestamp":1776668573000},"page":"117734","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A stabilization-free virtual element method for semilinear elliptic problems in two and three dimensions"],"prefix":"10.1016","volume":"487","author":[{"given":"Ou","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7765-8201","authenticated-orcid":false,"given":"Yanping","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.cam.2026.117734_bib0001","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1142\/S0218202512500492","article-title":"Basic principles of virtual element methods","volume":"23","author":"Beir\u00e3o da Veiga","year":"2013","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"10.1016\/j.cam.2026.117734_bib0002","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.camwa.2013.05.015","article-title":"Equivalent projectors for virtual element methods","volume":"66","author":"Ahmad","year":"2013","journal-title":"Comput. Math. Appl."},{"issue":"08","key":"10.1016\/j.cam.2026.117734_bib0003","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1142\/S021820251440003X","article-title":"The hitchhiker\u2019s guide to the virtual element method","volume":"24","author":"Beir\u00e3o da Veiga","year":"2014","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"4","key":"10.1016\/j.cam.2026.117734_bib0004","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1142\/S0218202516500160","article-title":"Virtual element method for general second-order elliptic problems on polygonal meshes","volume":"26","author":"Beir\u00e3o da Veiga","year":"2016","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"10.1016\/j.cam.2026.117734_bib0005","first-page":"1317","article-title":"Conforming and nonconforming virtual element methods for elliptic problems","volume":"37","author":"Cangiani","year":"2017","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"10.1016\/j.cam.2026.117734_bib0006","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1137\/13091141X","article-title":"A stream virtual element formulation of the Stokes problem on polygonal meshes","volume":"52","author":"Antonietti","year":"2014","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"10.1016\/j.cam.2026.117734_bib0007","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1051\/m2an\/2016032","article-title":"Divergence free virtual elements for the Stokes problem on polygonal meshes","volume":"51","author":"Beir\u00e3o da Veiga","year":"2017","journal-title":"ESAIM M2AN"},{"issue":"6","key":"10.1016\/j.cam.2026.117734_bib0008","doi-asserted-by":"crossref","first-page":"2110","DOI":"10.1002\/num.21982","article-title":"Virtual element methods for parabolic problems on polygonal meshes","volume":"31","author":"Vacca","year":"2015","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"5","key":"10.1016\/j.cam.2026.117734_bib0009","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1016\/j.camwa.2016.04.029","article-title":"Virtual element methods for hyperbolic problems on polygonal meshes","volume":"74","author":"Vacca","year":"2017","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"10.1016\/j.cam.2026.117734_bib0010","doi-asserted-by":"crossref","first-page":"794","DOI":"10.1137\/120874746","article-title":"Virtual elements for linear elasticity problems","volume":"51","author":"Beir\u00e3o da Veiga","year":"2013","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117734_bib0011","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.cma.2016.07.043","article-title":"Order preserving SUPG stabilization for the virtual element formulation of advection\u2013diffusion problems","volume":"311","author":"Benedetto","year":"2016","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0012","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.cma.2018.05.027","article-title":"SUPG Stabilization for the nonconforming virtual element method for advection\u2013diffusion\u2013reaction equations","volume":"340","author":"Berrone","year":"2018","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"8","key":"10.1016\/j.cam.2026.117734_bib0013","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1142\/S0218202517500233","article-title":"A residual a posteriori error estimate for the virtual element method","volume":"27","author":"Berrone","year":"2017","journal-title":"Math. Models Methods Appl. Sci."},{"key":"10.1016\/j.cam.2026.117734_bib0014","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2020.113663","article-title":"An enhanced VEM formulation for plane elasticity","volume":"376","author":"D\u2019Altri","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0015","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2023.108641","article-title":"A first-order stabilization-free virtual element method","volume":"142","author":"Berrone","year":"2023","journal-title":"Appl. Math. Lett."},{"issue":"5","key":"10.1016\/j.cam.2026.117734_bib0016","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1007\/s00466-023-02282-2","article-title":"A Hu\u2013Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics","volume":"71","author":"Lamperti","year":"2023","journal-title":"Comput. Mech."},{"key":"10.1016\/j.cam.2026.117734_bib0017","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.camwa.2024.02.024","article-title":"A lowest order stabilization-free mixed virtual element method","volume":"160","author":"Borio","year":"2024","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117734_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.116885","article-title":"A stabilization-free virtual element method based on divergence-free projections","volume":"424","author":"Berrone","year":"2024","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2025.117839","article-title":"Stabilization-free virtual element method for 2D second order elliptic equations","volume":"438","author":"Berrone","year":"2025","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2022.107971","article-title":"Comparison of standard and stabilization free virtual elements on anisotropic elliptic problems","volume":"129","author":"Berrone","year":"2022","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.cam.2026.117734_bib0021","unstructured":"A. Borio, M. Busetto, F. Marcon, SUPG-stabilized stabilization-free VEM: a numerical investigation, (2023). arXiv preprint arXiv: 2310.09180."},{"key":"10.1016\/j.cam.2026.117734_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.115784","article-title":"Stabilization-free serendipity virtual element method for plane elasticity","volume":"404","author":"Chen","year":"2023","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0023","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.camwa.2023.03.002","article-title":"Stabilization-free virtual element method for plane elasticity","volume":"138","author":"Chen","year":"2023","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117734_bib0024","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2024.116826","article-title":"3D stabilization-free virtual element method for linear elastic analysis","volume":"421","author":"Xu","year":"2024","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117734_bib0025","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.apnum.2019.05.021","article-title":"Virtual element method for semilinear elliptic problems on polygonal meshes","volume":"145","author":"Adak","year":"2019","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/j.cam.2026.117734_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.amc.2022.127402","article-title":"The nonconforming virtual element method for semilinear elliptic problems","volume":"433","author":"Xiao","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117734_bib0027","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.apnum.2023.01.009","article-title":"Two-grid virtual element discretization of semilinear elliptic problem","volume":"186","author":"Chen","year":"2023","journal-title":"Appl. Numer. Math."},{"issue":"5","key":"10.1016\/j.cam.2026.117734_bib0028","doi-asserted-by":"crossref","first-page":"1110","DOI":"10.1016\/j.camwa.2017.03.021","article-title":"High-order virtual element method on polyhedral meshes","volume":"74","author":"Da Veiga","year":"2017","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.cam.2026.117734_bib0029","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.camwa.2024.11.017","article-title":"Lowest order stabilization free virtual element method for the 2D poisson equation","volume":"177","author":"Berrone","year":"2025","journal-title":"Comput. Math. Appl."},{"issue":"9","key":"10.1016\/j.cam.2026.117734_bib0030","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1016\/j.camwa.2018.02.005","article-title":"Exploring high-order three dimensional virtual elements: bases and stabilizations","volume":"75","author":"Dassi","year":"2018","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"10.1016\/j.cam.2026.117734_bib0031","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10092-018-0249-4","article-title":"Some error analysis on virtual element methods","volume":"55","author":"Chen","year":"2018","journal-title":"Calcolo"},{"issue":"1","key":"10.1016\/j.cam.2026.117734_bib0032","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1515\/cmam-2022-0062","article-title":"Some estimates for virtual element methods in three dimensions","volume":"23","author":"Huang","year":"2023","journal-title":"Comput. Methods Appl. Math."},{"key":"10.1016\/j.cam.2026.117734_bib0033","unstructured":"Y. Yu, MVEM: a MATLAB software package for the virtual element methods, (2022). arXiv preprint arXiv: 2204.01339."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726003766?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726003766?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T11:42:43Z","timestamp":1783078963000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726003766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,12]]},"references-count":33,"alternative-id":["S0377042726003766"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117734","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A stabilization-free virtual element method for semilinear elliptic problems in two and three dimensions","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117734","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117734"}}