{"id":"https://openalex.org/W2970928918","doi":"https://doi.org/10.1515/cmam-2018-0197","title":"A Robust Finite Element Method for Elastic Vibration Problems","display_name":"A Robust Finite Element Method for Elastic Vibration Problems","publication_year":2019,"publication_date":"2019-08-28","ids":{"openalex":"https://openalex.org/W2970928918","doi":"https://doi.org/10.1515/cmam-2018-0197","mag":"2970928918"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0197","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0197","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","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/A5102690016","display_name":"Yuling Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuling Guo","raw_affiliation_strings":["School of Mathematical Sciences , and MOE-LSC , Shanghai Jiao Tong University , Shanghai 200240 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , and MOE-LSC , Shanghai Jiao Tong University , Shanghai 200240 , P. R. China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100651268","display_name":"Jianguo Huang","orcid":"https://orcid.org/0000-0003-0825-3056"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianguo Huang","raw_affiliation_strings":["School of Mathematical Sciences , and MOE-LSC , Shanghai Jiao Tong University , Shanghai 200240 , P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-0825-3056","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , and MOE-LSC , Shanghai Jiao Tong University , Shanghai 200240 , P. R. China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100651268"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.10250666,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"20","issue":"3","first_page":"481","last_page":"500"},"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":1.0,"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":1.0,"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":0.9998000264167786,"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":0.9994000196456909,"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/norm","display_name":"Norm (philosophy)","score":0.5111282467842102},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4570268988609314},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41525590419769287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39095351099967957}],"concepts":[{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5111282467842102},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4570268988609314},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41525590419769287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39095351099967957},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0197","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0197","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2643442054","display_name":null,"funder_award_id":"11571237","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"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":33,"referenced_works":["https://openalex.org/W776667372","https://openalex.org/W1971908487","https://openalex.org/W1986688379","https://openalex.org/W1992358193","https://openalex.org/W1997909686","https://openalex.org/W2008008473","https://openalex.org/W2019694950","https://openalex.org/W2026711180","https://openalex.org/W2029111242","https://openalex.org/W2037818443","https://openalex.org/W2038191139","https://openalex.org/W2038732088","https://openalex.org/W2039412304","https://openalex.org/W2049332222","https://openalex.org/W2051570063","https://openalex.org/W2055893851","https://openalex.org/W2072236487","https://openalex.org/W2073700150","https://openalex.org/W2073774784","https://openalex.org/W2075042757","https://openalex.org/W2075169689","https://openalex.org/W2089366649","https://openalex.org/W2108066087","https://openalex.org/W2136490233","https://openalex.org/W2462139209","https://openalex.org/W2519750562","https://openalex.org/W2592623476","https://openalex.org/W2963605320","https://openalex.org/W3196290810","https://openalex.org/W3204708751","https://openalex.org/W4256651668","https://openalex.org/W4298356938","https://openalex.org/W6605442296"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Abstract":[0],"A":[1,162],"robust":[2],"finite":[3],"element":[4],"method":[5,176],"is":[6,19,41,49,77,150],"introduced":[7],"for":[8,183],"solving":[9],"elastic":[10,158],"vibration":[11],"problems":[12],"in":[13,63,134],"two":[14],"dimensions.":[15],"The":[16],"temporal":[17],"discretization":[18,40],"carried":[20],"out":[21],"using":[22],"the":[23,38,44,56,59,64,128,132,144,147,153,157,174],"<m:math":[24,68,80,100],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[25,69,81,101],"<m:msub>":[26],"<m:mi>P</m:mi>":[27],"<m:mn>1</m:mn>":[28],"</m:msub>":[29],"</m:math>":[30,74,97,120],"{P_{1}}":[31],"-continuous":[32],"discontinuous":[33],"Galerkin":[34],"(CDG)":[35],"method,":[36],"while":[37],"spatial":[39],"based":[42],"on":[43,143],"Crouziex\u2013Raviart":[45],"(CR)":[46],"element.":[47],"It":[48],"shown":[50],"after":[51],"a":[52],"technical":[53],"derivation":[54],"that":[55],"error":[57,148],"of":[58,131,152,156,164,173],"displacement":[60],"(resp.":[61,67,99],"velocity)":[62],"energy":[65],"norm":[66],"<m:msup>":[70,109],"<m:mi>L</m:mi>":[71],"<m:mn>2</m:mn>":[72,111],"</m:msup>":[73,112],"{L^{2}}":[75],"norm)":[76],"bounded":[78],"by":[79],"<m:mrow>":[82,85,88,102,105,108],"<m:mi>O</m:mi>":[83,103],"<m:mo>\u2062</m:mo>":[84,104],"<m:mo":[86,93,106,116],"stretchy=\"false\">(</m:mo>":[87,107],"<m:mi>h</m:mi>":[89,110],"<m:mo>+</m:mo>":[90,113],"<m:mi>k</m:mi>":[91,114],"</m:mrow>":[92,95,96,115,118,119],"stretchy=\"false\">)</m:mo>":[94,117],"{O(h+k)}":[98],"{O(h^{2}+k)}":[121],"),":[122],"where":[123],"h":[124],"and":[125,136,177],"k":[126],"denote":[127],"mesh":[129],"sizes":[130],"subdivisions":[133],"space":[135],"time,":[137],"respectively.":[138],"Under":[139],"some":[140,178],"regularity":[141],"assumptions":[142],"exact":[145],"solution,":[146],"bound":[149],"independent":[151],"Lam\u00e9":[154],"coefficients":[155],"material":[159],"under":[160],"discussion.":[161],"series":[163],"numerical":[165,171],"results":[166],"are":[167],"offered":[168],"to":[169],"illustrate":[170],"performance":[172],"proposed":[175],"other":[179],"fully":[180],"discrete":[181],"methods":[182],"comparison.":[184]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}