{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T22:24:23Z","timestamp":1767219863937,"version":"3.48.0"},"reference-count":46,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/100007543","name":"Grantov\u00e1 Agentura, Univerzita Karlova","doi-asserted-by":"publisher","award":["PRIMUS\/22\/SCI\/014"],"award-info":[{"award-number":["PRIMUS\/22\/SCI\/014"]}],"id":[{"id":"10.13039\/100007543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    In this paper we develop a\n                    <jats:inline-formula id=\"j_cmam-2024-0153_ineq_9999\">\n                      <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <m:msup>\n                            <m:mi>C<\/m:mi>\n                            <m:mn>0<\/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-2024-0153_eq_0254.png\"\/>\n                        <jats:tex-math>{C^{0}}<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions.\nWe present a posteriori error analysis for this problem and derive a residual based error estimator.\nThe estimator is fully computable and we prove upper and lower bounds of the error which are explicit in the local mesh size.\nWe use the estimator to drive an adaptive mesh refinement algorithm.\nA handful of numerical test problems are carried out to study the performance of the proposed error indicator.\n                  <\/jats:p>","DOI":"10.1515\/cmam-2024-0153","type":"journal-article","created":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T17:20:31Z","timestamp":1763054431000},"page":"19-41","source":"Crossref","is-referenced-by-count":1,"title":["A Posteriori Error Analysis of the Virtual Element Method for Second-Order Quasilinear Elliptic PDEs"],"prefix":"10.1515","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7314-3120","authenticated-orcid":false,"given":"Scott","family":"Congreve","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Physics , 138735 Charles University , Sokolovsk\u00e1 83, 186 75 , Praha , Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5793-679X","authenticated-orcid":false,"given":"Alice","family":"Hodson","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Physics , 138735 Charles University , Sokolovsk\u00e1 83, 186 75 , Praha , Czech Republic"}]}],"member":"374","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"2025123121114987678_j_cmam-2024-0153_ref_001","doi-asserted-by":"crossref","unstructured":"D.  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Engrg. 142 (1997), no. 1\u20132, 1\u201388.","DOI":"10.1016\/S0045-7825(96)01107-3"},{"key":"2025123121114987678_j_cmam-2024-0153_ref_004","doi-asserted-by":"crossref","unstructured":"M. S.  Aln\u00e6s, A.  Logg, K. B.  \u00d8lgaard, M. E.  Rognes and G. N.  Wells,\nUnified form language: A domain-specific language for weak formulations and partial differential equations,\nACM Trans. Math. Software 40 (2014), no. 2, Paper No. 9.","DOI":"10.1145\/2566630"},{"key":"2025123121114987678_j_cmam-2024-0153_ref_005","doi-asserted-by":"crossref","unstructured":"P. F.  Antonietti, L.  Beir\u00e3o da Veiga, M.  Botti, G.  Vacca and M.  Verani,\nA virtual element method for non-Newtonian pseudoplastic Stokes flows,\nComput. Methods Appl. Mech. Engrg. 428 (2024), Article ID 117079.","DOI":"10.1016\/j.cma.2024.117079"},{"key":"2025123121114987678_j_cmam-2024-0153_ref_006","doi-asserted-by":"crossref","unstructured":"P. F.  Antonietti, L.  Beir\u00e3o da Veiga and G.  Manzini,\nThe Virtual Element Method and its Applications,\nSEMA SIMAI Springer Series 31,\nSpringer, Cham, 2022.","DOI":"10.1007\/978-3-030-95319-5"},{"key":"2025123121114987678_j_cmam-2024-0153_ref_007","doi-asserted-by":"crossref","unstructured":"P. F.  Antonietti, L.  Beir\u00e3o da Veiga, S.  Scacchi and M.  Verani,\nA \n                  \n                     \n                        \n                           C\n                           1\n                        \n                     \n                     \n                     {C^{1}}\n                  \n                virtual element method for the Cahn\u2013Hilliard equation with polygonal meshes,\nSIAM J. Numer. Anal. 54 (2016), no. 1, 34\u201356.","DOI":"10.1137\/15M1008117"},{"key":"2025123121114987678_j_cmam-2024-0153_ref_008","doi-asserted-by":"crossref","unstructured":"P. F.  Antonietti, N.  Bigoni and M.  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