{"id":"https://openalex.org/W4318701502","doi":"https://doi.org/10.1515/jnma-2022-0092","title":"Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation","display_name":"Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation","publication_year":2023,"publication_date":"2023-01-31","ids":{"openalex":"https://openalex.org/W4318701502","doi":"https://doi.org/10.1515/jnma-2022-0092"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2022-0092","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2022-0092","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2310.05648","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]},{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE","IN"],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":["Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany","Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India","Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037126929","display_name":"Benedikt Gr\u00e4\u00dfle","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Benedikt Gr\u00e4\u00dfle","raw_affiliation_strings":["Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Humboldt-Universit\u00e4t zu Berlin , 10099 Berlin , Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019365126","display_name":"Neela Nataraj","orcid":"https://orcid.org/0000-0002-5180-459X"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Neela Nataraj","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Bombay , Powai, Mumbai , 400076, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":["https://openalex.org/I162827531","https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":0.6026,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.58554723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"0","issue":"0","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.9643672704696655},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.8174260854721069},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7322503328323364},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6875392198562622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6377209424972534},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5956239700317383},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5831574201583862},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5564122796058655},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5385843515396118},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.43245822191238403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3411826193332672},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.1563321352005005},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10135909914970398},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08553200960159302}],"concepts":[{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.9643672704696655},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.8174260854721069},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7322503328323364},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6875392198562622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6377209424972534},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5956239700317383},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5831574201583862},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5564122796058655},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5385843515396118},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.43245822191238403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3411826193332672},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.1563321352005005},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10135909914970398},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08553200960159302},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jnma-2022-0092","is_oa":false,"landing_page_url":"https://doi.org/10.1515/jnma-2022-0092","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2310.05648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.05648","pdf_url":"https://arxiv.org/pdf/2310.05648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2310.05648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.05648","pdf_url":"https://arxiv.org/pdf/2310.05648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6499999761581421,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2953089827","display_name":null,"funder_award_id":"id 235","funder_id":"https://openalex.org/F4320330412","funder_display_name":"Scheme for Promotion of Academic and Research Collaboration"},{"id":"https://openalex.org/G5285342013","display_name":null,"funder_award_id":"151/22","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5448639614","display_name":null,"funder_award_id":"CA 151/22-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7522916683","display_name":null,"funder_award_id":"SPF/2020/000019","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320330412","display_name":"Scheme for Promotion of Academic and Research Collaboration","ror":null},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4318701502.pdf"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W280547473","https://openalex.org/W592368443","https://openalex.org/W1494982173","https://openalex.org/W1963865657","https://openalex.org/W1965104497","https://openalex.org/W1973103891","https://openalex.org/W1975039968","https://openalex.org/W1985605456","https://openalex.org/W1997926412","https://openalex.org/W1998803201","https://openalex.org/W2002410282","https://openalex.org/W2008916847","https://openalex.org/W2009985306","https://openalex.org/W2012900529","https://openalex.org/W2017073125","https://openalex.org/W2017366188","https://openalex.org/W2019685695","https://openalex.org/W2020552462","https://openalex.org/W2048407683","https://openalex.org/W2054401206","https://openalex.org/W2062819342","https://openalex.org/W2066976371","https://openalex.org/W2071036364","https://openalex.org/W2076740943","https://openalex.org/W2089093183","https://openalex.org/W2122461891","https://openalex.org/W2137365186","https://openalex.org/W2151369319","https://openalex.org/W2155803011","https://openalex.org/W2199169705","https://openalex.org/W2735401212","https://openalex.org/W2893822386","https://openalex.org/W2962763863","https://openalex.org/W2963027749","https://openalex.org/W2963175427","https://openalex.org/W2963817075","https://openalex.org/W3004866040","https://openalex.org/W3119118004","https://openalex.org/W3129604430","https://openalex.org/W3131705640","https://openalex.org/W3138346380","https://openalex.org/W3204708751","https://openalex.org/W4205815276","https://openalex.org/W4210300254","https://openalex.org/W4245007249","https://openalex.org/W4256592700","https://openalex.org/W4287185794","https://openalex.org/W4292166829","https://openalex.org/W4385684942","https://openalex.org/W4393855266"],"related_works":["https://openalex.org/W2503543076","https://openalex.org/W2982093746","https://openalex.org/W3043435143","https://openalex.org/W2158006240","https://openalex.org/W2610540941","https://openalex.org/W4299447939","https://openalex.org/W2332908959","https://openalex.org/W3007553996","https://openalex.org/W2023658642","https://openalex.org/W2006902680"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"abstract":[2,73],"property":[3],"(":[4,52],"H":[5,53,106],")":[6,54],"is":[7],"the":[8,18,29,49,56,97],"key":[9],"to":[10,55,76],"a":[11,13,57,68,101],"complete":[12],"priori":[14],"error":[15,59,70],"analysis":[16,60],"in":[17,28,105],"(discrete)":[19],"energy":[20],"norm":[21],"for":[22,38,96],"several":[23],"nonstandard":[24,34],"finite":[25,35],"element":[26,36],"methods":[27,37],"recent":[30],"work":[31],"[Lowest-order":[32],"equivalent":[33],"biharmonic":[39,98],"plates,":[40],"Carstensen":[41],"and":[42,61,64],"Nataraj,":[43],"M2AN,":[44],"2022].":[45],"This":[46],"paper":[47],"investigates":[48],"impact":[50],"of":[51,80],"posteriori":[58,69],"establishes":[62],"known":[63],"novel":[65],"explicit":[66],"residualbased":[67],"estimates.":[71],"The":[72],"framework":[74],"applies":[75],"Morley,":[77],"two":[78],"versions":[79],"discontinuous":[81],"Galerkin,":[82],"C":[83],"0":[84],"interior":[85,93],"penalty,":[86],"as":[87,89],"well":[88],"weakly":[90],"overpenalized":[91],"symmetric":[92],"penalty":[94],"schemes":[95],"equation":[99],"with":[100],"general":[102],"source":[103],"term":[104],"\u22122":[107],"(\u03a9).":[108]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
