{"id":"https://openalex.org/W3174321950","doi":"https://doi.org/10.1090/mcom/3739","title":"A finite element elasticity complex in three dimensions","display_name":"A finite element elasticity complex in three dimensions","publication_year":2022,"publication_date":"2022-02-23","ids":{"openalex":"https://openalex.org/W3174321950","doi":"https://doi.org/10.1090/mcom/3739","mag":"3174321950"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3739","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3739","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5100336427","display_name":"Long Chen","orcid":"https://orcid.org/0000-0003-0184-5446"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Long Chen","raw_affiliation_strings":["Department of Mathematics, University of California at Irvine, Irvine, California 92697"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at Irvine, Irvine, California 92697","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082483290","display_name":"Xuehai Huang","orcid":"https://orcid.org/0000-0003-2966-7426"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuehai Huang","raw_affiliation_strings":["School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, People\u00e2\u0080\u0099s Republic of China","School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China","institution_ids":["https://openalex.org/I181679659"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0157,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.91261087,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"91","issue":"337","first_page":"2095","last_page":"2127"},"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":0.9986000061035156,"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":0.9986000061035156,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6377815008163452},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43530362844467163},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4060114026069641},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38615676760673523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37468481063842773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3513765037059784},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09853553771972656}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6377815008163452},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43530362844467163},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4060114026069641},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38615676760673523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37468481063842773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3513765037059784},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09853553771972656},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3739","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3739","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt16m1p493","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/16m1p493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, vol 91, iss 337","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1327987502","display_name":null,"funder_award_id":"11771338","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G1814487920","display_name":null,"funder_award_id":"12171300","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2014301466","display_name":null,"funder_award_id":"2019110066","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2166764095","display_name":null,"funder_award_id":"2012465","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2552195495","display_name":null,"funder_award_id":"2019110066","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G274310516","display_name":null,"funder_award_id":"21ZR1480500","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2809486088","display_name":"\u5916\u5fae\u79ef\u5206\u7406\u8bba\u53ca\u9ad8\u9636\u692d\u5706\u578b\u65b9\u7a0b\u9ad8\u6548\u6570\u503c\u7b97\u6cd5\u7684\u7814\u7a76","funder_award_id":"11771338","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3046541435","display_name":null,"funder_award_id":"11771338","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3275005723","display_name":null,"funder_award_id":"2012465","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3304683657","display_name":null,"funder_award_id":"2012465","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G5065594398","display_name":null,"funder_award_id":"2019110066","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5213618898","display_name":null,"funder_award_id":"21ZR1480500","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5667877555","display_name":null,"funder_award_id":"11771338","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G570771576","display_name":"Novel Virtual Element Methods with Applications in Interface Problems","funder_award_id":"1913080","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5851791200","display_name":null,"funder_award_id":"1913080","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6035216221","display_name":null,"funder_award_id":"1913080","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G6123396132","display_name":null,"funder_award_id":"2019110066","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6678179562","display_name":null,"funder_award_id":"12171300","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7110634559","display_name":null,"funder_award_id":"12171300","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G7576143021","display_name":null,"funder_award_id":"1913080","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7634426117","display_name":"Fast Optimization Methods and Application to Data Science and Nonlinear Partial Differential Equations","funder_award_id":"2012465","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7978699620","display_name":null,"funder_award_id":"21ZR1480500","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8796644149","display_name":"\u79bb\u6563\u5171\u5f62\u5f20\u91cf\u5fae\u5206\u590d\u5f62\u7684\u6784\u9020\u4e0e\u5e94\u7528","funder_award_id":"21ZR1480500","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G8906950000","display_name":null,"funder_award_id":"12171300","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W206256087","https://openalex.org/W629836974","https://openalex.org/W1874307083","https://openalex.org/W1966811893","https://openalex.org/W1975039968","https://openalex.org/W1978591107","https://openalex.org/W2007903663","https://openalex.org/W2014744421","https://openalex.org/W2023930096","https://openalex.org/W2035837270","https://openalex.org/W2100999330","https://openalex.org/W2131341034","https://openalex.org/W2138486270","https://openalex.org/W2156629649","https://openalex.org/W2266218136","https://openalex.org/W2549082561","https://openalex.org/W2613239920","https://openalex.org/W2785094756","https://openalex.org/W2810477279","https://openalex.org/W2882976948","https://openalex.org/W2906022956","https://openalex.org/W2911441929","https://openalex.org/W2951909736","https://openalex.org/W2952057749","https://openalex.org/W2963009999","https://openalex.org/W2963397795","https://openalex.org/W2963773676","https://openalex.org/W2964125407","https://openalex.org/W2990940994","https://openalex.org/W2998796568","https://openalex.org/W3023995120","https://openalex.org/W3043878674","https://openalex.org/W3046476175","https://openalex.org/W3080196891","https://openalex.org/W3085487270","https://openalex.org/W3092595374","https://openalex.org/W3101547432","https://openalex.org/W3103476862","https://openalex.org/W3116158617","https://openalex.org/W3120658540","https://openalex.org/W3127239180","https://openalex.org/W3142894564","https://openalex.org/W3194777423","https://openalex.org/W4226290109","https://openalex.org/W4286695162","https://openalex.org/W4289317684"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"finite":[1,35,39,56,96,157,256],"element":[2,36,40,57,61,97,257],"elasticity":[3,204,208],"complex":[4,205,209,259,286],"on":[5,159],"tetrahedral":[6,160],"meshes":[7,161],"and":[8,178,206,244,260],"the":[9,38,45,59,118,128,169,172,179,182,185,214,219,252],"corresponding":[10],"commutative":[11],"diagram":[12],"are":[13,171,210,247,287],"devised.":[14],"The":[15,53,65,165,202,216],"<inline-formula":[16,69,102,130,186,220,261],"content-type=\"math/mathml\">":[17,70,103,131,187,221,262],"<mml:math":[18,71,104,132,188,222,263],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,72,105,133,189,223,264],"alttext=\"upper":[20,73,134],"H":[21,74,135],"Superscript":[22],"1\">":[23],"<mml:semantics>":[24,80,107,141,193,227,271],"<mml:msup>":[25],"<mml:mi>H</mml:mi>":[26,82,143],"<mml:mn>1</mml:mn>":[27],"</mml:msup>":[28],"<mml:annotation":[29,89,109,150,195,229,279],"encoding=\"application/x-tex\">H^1</mml:annotation>":[30],"</mml:semantics>":[31,92,111,153,198,232,283],"</mml:math>":[32,93,112,154,199,233,284],"</inline-formula>":[33,94,113,155,200,234,285],"conforming":[34],"is":[37,58,117,236],"developed":[41],"by":[42],"Neilan":[43],"for":[44,62,114],"velocity":[46],"field":[47],"in":[48],"a":[49,239],"discrete":[50],"Stokes":[51],"complex.":[52],"symmetric":[54,115],"div-conforming":[55],"Hu-Zhang":[60],"stress":[63],"tensors.":[64],"construction":[66,124,170],"of":[67,98,120,168,174,181,184,218],"an":[68],"left-parenthesis":[75,136],"i":[76,137,266,269],"n":[77,138,191,225],"c":[78,139],"right-parenthesis\">":[79,140],"<mml:mrow>":[81,142,272],"<mml:mo":[83,86,144,147],"stretchy=\"false\">(</mml:mo>":[84,145],"<mml:mi>inc</mml:mi>":[85,146,194,228],"stretchy=\"false\">)</mml:mo>":[87,148],"</mml:mrow>":[88,149,278],"encoding=\"application/x-tex\">H(\\operatorname":[90,151],"{inc})</mml:annotation>":[91,152],"-conforming":[95,156],"minimum":[99],"polynomial":[100,175,203],"degree":[101],"alttext=\"6\">":[106],"<mml:mn>6</mml:mn>":[108],"encoding=\"application/x-tex\">6</mml:annotation>":[110],"tensors":[116],"focus":[119],"this":[121],"paper.":[122],"Our":[123],"appears":[125],"to":[126,212,250],"be":[127],"first":[129],"elements":[158],"without":[162],"further":[163],"splitting.":[164],"key":[166],"tools":[167],"decomposition":[173],"tensor":[176],"spaces":[177],"characterization":[180],"trace":[183,217],"alttext=\"i":[190,224],"c\">":[192,226],"encoding=\"application/x-tex\">\\operatorname":[196,230,280],"{inc}</mml:annotation>":[197,231],"operator.":[201],"Koszul":[207],"created":[211],"derive":[213],"decomposition.":[215],"operator":[235],"induced":[237],"from":[238],"Green\u2019s":[240],"identity.":[241],"Trace":[242],"complexes":[243,246],"bubble":[245],"also":[248],"derived":[249],"facilitate":[251],"construction.":[253],"Two-dimensional":[254],"smooth":[255],"Hessian":[258],"alttext=\"d":[265],"v":[267],"d":[268],"v\">":[270],"<mml:mi>div</mml:mi>":[273,277],"<mml:mo>":[274],"\u2061":[275],"</mml:mo>":[276],"{div}\\operatorname":[281],"{div}</mml:annotation>":[282],"constructed.":[288]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}