{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:46Z","timestamp":1747198066032,"version":"3.40.5"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,10,1]]},"abstract":"Abstract<\/jats:title>\n We construct three H-curl-curl finite elements.\nThe \n \n \n \n P<\/m:mi>\n 2<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{2}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n \n \n P<\/m:mi>\n 3<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{3}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> vector finite element spaces are both\nenriched by one common \n \n \n \n P<\/m:mi>\n 4<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{4}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bubble and their local degrees of freedom are 13 and 21, respectively.\nAs there does not exist any \n \n \n \n P<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{1}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> H-curl-curl conforming finite element, the \n \n \n \n P<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{1}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> H-curl-curl nonconforming finite element is constructed\nwith three additional \n \n \n \n P<\/m:mi>\n 4<\/m:mn>\n <\/m:msub>\n <\/m:math>\n \n P_{4}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bubbles.\nNumerical tests are presented, confirming the conformity and the optimal order of convergence.<\/jats:p>","DOI":"10.1515\/cmam-2023-0140","type":"journal-article","created":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T16:01:07Z","timestamp":1696348867000},"page":"1021-1032","source":"Crossref","is-referenced-by-count":0,"title":["Three Low Order H-Curl-Curl Finite Elements on Triangular Meshes"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1114-4179","authenticated-orcid":false,"given":"Shangyou","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences , University of Delaware , Newark , DE 19716 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"key":"2024100217254122224_j_cmam-2023-0140_ref_001","doi-asserted-by":"crossref","unstructured":"V. Girault and P.-A. Raviart,\nFinite Element Methods for Navier\u2013Stokes Equations. Theory and Algorithms,\nSpringer Ser. Comput. Math. 5,\nSpringer, Berlin, 1986.","DOI":"10.1007\/978-3-642-61623-5"},{"key":"2024100217254122224_j_cmam-2023-0140_ref_002","doi-asserted-by":"crossref","unstructured":"K. Hu, Q. Zhang and Z. Zhang,\nSimple curl-curl-conforming finite elements in two dimensions,\nSIAM J. Sci. Comput. 42 (2020), no. 6, A3859\u2013A3877.","DOI":"10.1137\/20M1333390"},{"key":"2024100217254122224_j_cmam-2023-0140_ref_003","doi-asserted-by":"crossref","unstructured":"L. R. Scott and S. Zhang,\nFinite element interpolation of nonsmooth functions satisfying boundary conditions,\nMath. Comp. 54 (1990), no. 190, 483\u2013493.","DOI":"10.1090\/S0025-5718-1990-1011446-7"},{"key":"2024100217254122224_j_cmam-2023-0140_ref_004","unstructured":"L. Wang, Q. Zhang, J. Sun and Z. Zhang,\nA priori and a posterior error estimations of quad-curl eigenvalue problems in 2D,\npreprint (2020), https:\/\/arxiv.org\/abs\/2007.01330."},{"key":"2024100217254122224_j_cmam-2023-0140_ref_005","doi-asserted-by":"crossref","unstructured":"Q. Zhang, L. Wang and Z. Zhang,\nH(curl2)-conforming finite elements in 2 dimensions and applications to the quad-curl problem,\nSIAM J. Sci. Comput. 41 (2019), no. 3, A1527\u2013A1547.","DOI":"10.1137\/18M1199988"},{"key":"2024100217254122224_j_cmam-2023-0140_ref_006","doi-asserted-by":"crossref","unstructured":"B. Zheng, Q. Hu and J. Xu,\nA nonconforming finite element method for fourth order curl equations in R3,\nMath. Comp. 80 (2011), no. 276, 1871\u20131886.","DOI":"10.1090\/S0025-5718-2011-02480-4"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0140\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0140\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T17:26:23Z","timestamp":1727889983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2023-0140\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,4]]},"references-count":6,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,1,2]]},"published-print":{"date-parts":[[2024,10,1]]}},"alternative-id":["10.1515\/cmam-2023-0140"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2023-0140","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"type":"print","value":"1609-4840"},{"type":"electronic","value":"1609-9389"}],"subject":[],"published":{"date-parts":[[2023,10,4]]}}}