{"id":"https://openalex.org/W3193093944","doi":"https://doi.org/10.1007/s10915-021-01597-7","title":"H$$^2$$-Korn\u2019s Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model","display_name":"H$$^2$$-Korn\u2019s Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model","publication_year":2021,"publication_date":"2021-08-04","ids":{"openalex":"https://openalex.org/W3193093944","doi":"https://doi.org/10.1007/s10915-021-01597-7","mag":"3193093944"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01597-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01597-7","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/A5100442424","display_name":"Hongliang Li","orcid":"https://orcid.org/0000-0003-0348-7910"},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongliang Li","raw_affiliation_strings":["School of Mathematics and Science, Sichuan Normal University, Chengdu, 610066, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Science, Sichuan Normal University, Chengdu, 610066, China","institution_ids":["https://openalex.org/I63354593"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111939462","display_name":"Pingbing Ming","orcid":"https://orcid.org/0000-0002-0779-1576"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Pingbing Ming","raw_affiliation_strings":["LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS Chinese Academy of Sciences, No. 55, East Road Zhong-Guan-Cun, Beijing, 100190, China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS Chinese Academy of Sciences, No. 55, East Road Zhong-Guan-Cun, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100670139","display_name":"Huiyu Wang","orcid":"https://orcid.org/0000-0001-7855-9769"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huiyu Wang","raw_affiliation_strings":["Beijing 101 Middle School, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing 101 Middle School, Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111939462"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.4353,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.53779342,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"88","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9994000196456909,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.8657124638557434},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6505351066589355},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6393121480941772},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6063680052757263},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5470786690711975},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5407599806785583},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5192446708679199},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47726553678512573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47234097123146057},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3316657543182373},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2978888750076294},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.10339057445526123}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8657124638557434},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6505351066589355},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6393121480941772},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6063680052757263},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5470786690711975},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5407599806785583},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5192446708679199},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47726553678512573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47234097123146057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3316657543182373},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2978888750076294},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.10339057445526123},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-021-01597-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01597-7","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.550000011920929}],"awards":[{"id":"https://openalex.org/G4226093039","display_name":null,"funder_award_id":"11971467","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W135694094","https://openalex.org/W206256087","https://openalex.org/W325210746","https://openalex.org/W333643410","https://openalex.org/W1492326914","https://openalex.org/W1498345005","https://openalex.org/W1548066750","https://openalex.org/W1586623601","https://openalex.org/W1966513386","https://openalex.org/W1978591107","https://openalex.org/W1981014263","https://openalex.org/W1983001190","https://openalex.org/W1984980836","https://openalex.org/W1985858216","https://openalex.org/W1990225789","https://openalex.org/W2009985306","https://openalex.org/W2014293274","https://openalex.org/W2020244851","https://openalex.org/W2020552462","https://openalex.org/W2038026052","https://openalex.org/W2041523977","https://openalex.org/W2050083144","https://openalex.org/W2056381343","https://openalex.org/W2064991465","https://openalex.org/W2065164098","https://openalex.org/W2066060458","https://openalex.org/W2073370369","https://openalex.org/W2080474385","https://openalex.org/W2084113519","https://openalex.org/W2086160648","https://openalex.org/W2091955543","https://openalex.org/W2106974008","https://openalex.org/W2110176271","https://openalex.org/W2119134040","https://openalex.org/W2130350269","https://openalex.org/W2131208755","https://openalex.org/W2158240664","https://openalex.org/W2164000452","https://openalex.org/W2265870922","https://openalex.org/W2314742673","https://openalex.org/W2322166453","https://openalex.org/W2589767494","https://openalex.org/W2890918203","https://openalex.org/W2917203384","https://openalex.org/W2963027749","https://openalex.org/W2963262008","https://openalex.org/W2963817075","https://openalex.org/W2976261942","https://openalex.org/W2980346834","https://openalex.org/W3004711689","https://openalex.org/W3150221135","https://openalex.org/W3154878168","https://openalex.org/W3204708751","https://openalex.org/W4243738351","https://openalex.org/W4249945978","https://openalex.org/W4301313402","https://openalex.org/W6600291067"],"related_works":["https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W1987870972","https://openalex.org/W2489141557","https://openalex.org/W2376821690","https://openalex.org/W2789181986","https://openalex.org/W4302420697"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}
