{"id":"https://openalex.org/W2737775198","doi":"https://doi.org/10.1007/s10915-017-0501-0","title":"A $$C^0$$ Linear Finite Element Method for Biharmonic Problems","display_name":"A $$C^0$$ Linear Finite Element Method for Biharmonic Problems","publication_year":2017,"publication_date":"2017-07-20","ids":{"openalex":"https://openalex.org/W2737775198","doi":"https://doi.org/10.1007/s10915-017-0501-0","mag":"2737775198"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-017-0501-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-017-0501-0","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044223666","display_name":"Hailong Guo","orcid":"https://orcid.org/0000-0001-7621-2315"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hailong Guo","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100406520","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-0531-9112"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China","Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053903143","display_name":"Qingsong Zou","orcid":"https://orcid.org/0000-0002-0710-7893"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qingsong Zou","raw_affiliation_strings":["School of Data and Computer Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Data and Computer Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053903143"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.4662,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.78727329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"74","issue":"3","first_page":"1397","last_page":"1422"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.9832899570465088},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.9651631116867065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8658515214920044},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.79038405418396},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5207207798957825},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5195255875587463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5038284659385681},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4911467730998993},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.47196921706199646},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4631931185722351},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4392617642879486},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.4346834421157837},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4320130944252014},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20780596137046814},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.06896209716796875}],"concepts":[{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.9832899570465088},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9651631116867065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8658515214920044},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.79038405418396},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5207207798957825},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5195255875587463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5038284659385681},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4911467730998993},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47196921706199646},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4631931185722351},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4392617642879486},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.4346834421157837},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4320130944252014},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20780596137046814},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.06896209716796875},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-017-0501-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-017-0501-0","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1634303658","display_name":null,"funder_award_id":"11571384","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2042984870","display_name":null,"funder_award_id":"11428103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2746842099","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4472046779","display_name":"\u82e5\u5e72\u5177\u6709\u5f31\u5bfc\u6570\u7684\u65b0\u578b\u8ba1\u7b97\u65b9\u6cd5\u7684\u68af\u5ea6\u91cd\u6784","funder_award_id":"11471031","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6682922420","display_name":null,"funder_award_id":"1419040","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1585767079","https://openalex.org/W1807403118","https://openalex.org/W1970753375","https://openalex.org/W1975039968","https://openalex.org/W1994336408","https://openalex.org/W1995404822","https://openalex.org/W2003049157","https://openalex.org/W2017073125","https://openalex.org/W2021157249","https://openalex.org/W2041523977","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2046130209","https://openalex.org/W2048248082","https://openalex.org/W2050178911","https://openalex.org/W2055009689","https://openalex.org/W2061130734","https://openalex.org/W2065479689","https://openalex.org/W2076586533","https://openalex.org/W2090400645","https://openalex.org/W2157121531","https://openalex.org/W2299929859","https://openalex.org/W2505585705","https://openalex.org/W2537790887","https://openalex.org/W2547325909","https://openalex.org/W2736928288","https://openalex.org/W3204708751","https://openalex.org/W4285719527","https://openalex.org/W6603867535"],"related_works":["https://openalex.org/W2503543076","https://openalex.org/W2001758285","https://openalex.org/W2737775198","https://openalex.org/W2070923604","https://openalex.org/W1975406625","https://openalex.org/W111458089","https://openalex.org/W2005628797","https://openalex.org/W2009926812","https://openalex.org/W2011851063","https://openalex.org/W2074783170"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
