{"id":"https://openalex.org/W3135225428","doi":"https://doi.org/10.1137/21m1404235","title":"Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System","display_name":"Conforming Finite Element DIVDIV Complexes and the Application for the Linearized Einstein--Bianchi System","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W3135225428","doi":"https://doi.org/10.1137/21m1404235","mag":"3135225428"},"language":"en","primary_location":{"id":"doi:10.1137/21m1404235","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1404235","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5028500115","display_name":"Jun Hu","orcid":"https://orcid.org/0000-0002-4565-3000"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Hu","raw_affiliation_strings":["Peking University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010142273","display_name":"Yizhou Liang","orcid":"https://orcid.org/0000-0001-6318-1708"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yizhou Liang","raw_affiliation_strings":["Peking University"],"raw_orcid":"https://orcid.org/0000-0001-6318-1708","affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101729708","display_name":"Rui Ma","orcid":"https://orcid.org/0000-0002-6534-6112"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rui Ma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5028500115"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":2.3258,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86621363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"3","first_page":"1307","last_page":"1330"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T11416","display_name":"Numerical methods for differential equations","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/finite-element-method","display_name":"Finite element method","score":0.7700722217559814},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7059893608093262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6406997442245483},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6277821063995361},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.5086539387702942},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4827679693698883},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.47550898790359497},{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.47031843662261963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4587995409965515},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.44267648458480835},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4388500154018402},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3705747723579407},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3301767110824585},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29291558265686035},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07261186838150024}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7700722217559814},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7059893608093262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6406997442245483},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6277821063995361},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.5086539387702942},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4827679693698883},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.47550898790359497},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.47031843662261963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4587995409965515},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44267648458480835},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4388500154018402},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3705747723579407},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3301767110824585},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29291558265686035},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07261186838150024},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1404235","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1404235","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1631108597","display_name":null,"funder_award_id":"STA 402/14-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8051312613","display_name":null,"funder_award_id":"11421101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G873693170","display_name":null,"funder_award_id":"11625101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W592911714","https://openalex.org/W2014744421","https://openalex.org/W2015945757","https://openalex.org/W2023930096","https://openalex.org/W2138486270","https://openalex.org/W2258217272","https://openalex.org/W2283070814","https://openalex.org/W2549082561","https://openalex.org/W2902365405","https://openalex.org/W2906022956","https://openalex.org/W2911441929","https://openalex.org/W2962941889","https://openalex.org/W2963180864","https://openalex.org/W2963397795","https://openalex.org/W3023995120","https://openalex.org/W3043878674","https://openalex.org/W3046476175","https://openalex.org/W3092595374","https://openalex.org/W3101547432","https://openalex.org/W3116158617","https://openalex.org/W3120658540","https://openalex.org/W3127239180","https://openalex.org/W3142894564","https://openalex.org/W3174321950","https://openalex.org/W3194777423"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2010821947","https://openalex.org/W4234008889","https://openalex.org/W1573186872","https://openalex.org/W2071722255","https://openalex.org/W2165887158","https://openalex.org/W2352023866","https://openalex.org/W2021654023","https://openalex.org/W2350569191"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,74,79],"first":[4],"family":[5],"of":[6,24,46],"conforming":[7],"finite":[8,21,43,60],"element":[9,22,44,61],"$\\ddiv\\ddiv$":[10],"complexes":[11,62],"on":[12],"tetrahedral":[13],"grids":[14],"in":[15],"three":[16],"dimensions.":[17],"In":[18],"these":[19,59],"complexes,":[20],"spaces":[23,45],"$H(\\ddiv\\ddiv,\\Omega;\\Sbb)$":[25],"are":[26,51,63],"from":[27],"a":[28,66],"recent":[29],"article":[30],"[L.":[31],"Chen":[32],"and":[33,49],"X.":[34],"Huang,":[35],"Math.":[36],"Comp.,":[37],"91":[38],"(2022),":[39],"pp.":[40],"1107--1142]":[41],"while":[42],"both":[47],"$H(\\sym\\ccurl,\\Omega;\\Tbb)$":[48],"$H^1(\\Omega;\\R^3)$":[50],"newly":[52],"constructed":[53],"here.":[54],"It":[55],"is":[56],"proved":[57],"that":[58],"exact.":[64],"As":[65],"result,":[67],"they":[68],"can":[69],"be":[70],"used":[71],"to":[72],"discretize":[73],"linearized":[75],"Einstein--Bianchi":[76],"system":[77],"within":[78],"dual":[80],"formulation.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
