{"id":"https://openalex.org/W3043878674","doi":"https://doi.org/10.1090/mcom/3700","title":"Finite elements for divdiv conforming symmetric tensors in three dimensions","display_name":"Finite elements for divdiv conforming symmetric tensors in three dimensions","publication_year":2021,"publication_date":"2021-12-10","ids":{"openalex":"https://openalex.org/W3043878674","doi":"https://doi.org/10.1090/mcom/3700","mag":"3043878674"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3700","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3700","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/A5100336409","display_name":"Long Chen","orcid":"https://orcid.org/0000-0002-6877-8252"},"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":2.4305,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.89473684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"91","issue":"335","first_page":"1107","last_page":"1142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9785000085830688,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6077750325202942},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.4485814869403839},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44765955209732056},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41046756505966187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36894840002059937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3582802414894104},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09882986545562744}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6077750325202942},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.4485814869403839},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44765955209732056},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41046756505966187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36894840002059937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3582802414894104},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09882986545562744},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3700","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3700","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"}],"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/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/G3562104867","display_name":null,"funder_award_id":"DMS-1913080","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3814140723","display_name":null,"funder_award_id":"DMS-2012465","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/G5375488065","display_name":null,"funder_award_id":"DMS-2012465","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5378369553","display_name":null,"funder_award_id":"DMS-2012465","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"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/G6123396132","display_name":null,"funder_award_id":"2019110066","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6274280442","display_name":null,"funder_award_id":"DMS-2012465","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6533678207","display_name":null,"funder_award_id":"DMS-1913080","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"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/G7558617164","display_name":null,"funder_award_id":"DMS-1913080","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"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"},{"id":"https://openalex.org/G8914113466","display_name":null,"funder_award_id":"DMS-1913080","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":27,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W592911714","https://openalex.org/W1874307083","https://openalex.org/W1968500177","https://openalex.org/W2041523977","https://openalex.org/W2164402335","https://openalex.org/W2258217272","https://openalex.org/W2460912296","https://openalex.org/W2518907075","https://openalex.org/W2902365405","https://openalex.org/W2963009999","https://openalex.org/W2963180864","https://openalex.org/W2964125407","https://openalex.org/W3023995120","https://openalex.org/W3032617580","https://openalex.org/W3046476175","https://openalex.org/W3092595374","https://openalex.org/W3100812035","https://openalex.org/W3104138274","https://openalex.org/W3116158617","https://openalex.org/W3120658540","https://openalex.org/W3135225428","https://openalex.org/W3150163258","https://openalex.org/W3174321950","https://openalex.org/W3194777423","https://openalex.org/W3204708751","https://openalex.org/W6600566992"],"related_works":["https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2625833328"],"abstract_inverted_index":{"Finite":[0],"element":[1,175,192,234],"spaces":[2,52,103],"on":[3,182],"a":[4,143,190,232],"tetrahedron":[5],"are":[6,46,94,104,140],"constructed":[7,224],"for":[8,112,193],"<inline-formula":[9,62,114,194,235],"content-type=\"math/mathml\">":[10,63,115,195,236],"<mml:math":[11,64,116,196,237],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,65,117,197,238],"alttext=\"d":[13,66,118,239],"i":[14,17,67,70,119,122,240,243],"v":[15,68,120,241],"d":[16,69,121,242],"v\">":[18,71,123,244],"<mml:semantics>":[19,72,124,205,245],"<mml:mrow>":[20,73,125,206,246],"<mml:mi>div</mml:mi>":[21,25,74,78,126,130,247,251],"<mml:mo>":[22,75,127,248],"\u2061":[23,76,128,249],"</mml:mo>":[24,77,129,250],"</mml:mrow>":[26,79,131,214,252],"<mml:annotation":[27,80,132,215,253],"encoding=\"application/x-tex\">\\operatorname":[28,81,133,254],"{div}\\operatorname":[29,82,134,255],"{div}</mml:annotation>":[30,83,135,256],"</mml:semantics>":[31,84,136,217,257],"</mml:math>":[32,85,137,218,258],"</inline-formula>":[33,86,138,219,259],"-conforming":[34,220],"symmetric":[35,173],"tensors":[36,222],"in":[37,268],"three":[38,269],"dimensions.":[39],"The":[40],"key":[41],"tools":[42],"of":[43,49,56,98,154,158,170],"the":[44,47,54,57,61,107,113,147,159,164,168,172,183,226,264],"construction":[45],"decomposition":[48],"polynomial":[50,92,99,108],"tensor":[51,102,160,174],"and":[53,89,101,181],"characterization":[55],"trace":[58,151],"operators.":[59],"First,":[60],"Hilbert":[87],"complex":[88],"its":[90],"corresponding":[91],"complexes":[93],"presented.":[95],"Several":[96],"decompositions":[97],"vector":[100],"derived":[105],"from":[106],"complexes.":[109],"Second,":[110],"traces":[111],"operator":[139],"characterized":[141],"through":[142],"Green\u2019s":[144],"identity.":[145],"Besides":[146],"normal-normal":[148],"component,":[149],"another":[150],"involving":[152],"combination":[153],"first":[155],"order":[156],"derivatives":[157],"is":[161,176,223,271],"continuous":[162,178],"across":[163],"face.":[165],"Due":[166],"to":[167,186],"smoothness":[169],"polynomials,":[171],"also":[177],"at":[179],"vertices,":[180],"plane":[184],"orthogonal":[185],"each":[187],"edge.":[188],"Besides,":[189],"finite":[191,233],"alttext=\"s":[198],"y":[199],"m":[200],"c":[201],"u":[202],"r":[203],"l\">":[204],"<mml:mi>s</mml:mi>":[207],"<mml:mi>y</mml:mi>":[208],"<mml:mi>m</mml:mi>":[209],"<mml:mi>c</mml:mi>":[210],"<mml:mi>u</mml:mi>":[211],"<mml:mi>r</mml:mi>":[212],"<mml:mi>l</mml:mi>":[213],"encoding=\"application/x-tex\">symcurl</mml:annotation>":[216],"trace-free":[221],"following":[225],"same":[227],"approach.":[228],"Putting":[229],"all":[230],"together,":[231],"complex,":[260,267],"as":[261,263],"well":[262],"bubble":[265],"functions":[266],"dimensions":[270],"established.":[272]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
