{"id":"https://openalex.org/W2090503985","doi":"https://doi.org/10.1080/00207160.2015.1011142","title":"A new Galerkin spectral element method for fourth-order boundary value problems","display_name":"A new Galerkin spectral element method for fourth-order boundary value problems","publication_year":2015,"publication_date":"2015-01-23","ids":{"openalex":"https://openalex.org/W2090503985","doi":"https://doi.org/10.1080/00207160.2015.1011142","mag":"2090503985"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1011142","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1011142","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5048964534","display_name":"Tao Sun","orcid":"https://orcid.org/0000-0003-0913-581X"},"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":true,"raw_author_name":"Tao Sun","raw_affiliation_strings":["School of Statistics and Mathematics, Shanghai Finance University, Shanghai 201209, China","School of Statistics and Mathematics, Shanghai Finance University, Shanghai201209, China#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Shanghai Finance University, Shanghai 201209, China","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"School of Statistics and Mathematics, Shanghai Finance University, Shanghai201209, China#TAB#","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084338992","display_name":"Lijun Yi","orcid":"https://orcid.org/0000-0002-2922-5508"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lijun Yi","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","Department of Mathematics, Shanghai Normal University, Shanghai200234, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai200234, China#TAB#","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048964534"],"corresponding_institution_ids":["https://openalex.org/I181679659"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.06066457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"93","issue":"6","first_page":"915","last_page":"928"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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/galerkin-method","display_name":"Galerkin method","score":0.800490140914917},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.7696555852890015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7476659417152405},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.6333863139152527},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.6096280813217163},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.5947200059890747},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5661145448684692},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5507829189300537},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5276468992233276},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4983961582183838},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4637044072151184},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4521770477294922},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4499753415584564},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43756037950515747},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.2157093584537506},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.05186071991920471}],"concepts":[{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.800490140914917},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.7696555852890015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7476659417152405},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.6333863139152527},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.6096280813217163},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.5947200059890747},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5661145448684692},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5507829189300537},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5276468992233276},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4983961582183838},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4637044072151184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4521770477294922},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4499753415584564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43756037950515747},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2157093584537506},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.05186071991920471},{"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1011142","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1011142","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W106404678","https://openalex.org/W321261355","https://openalex.org/W1537887709","https://openalex.org/W1600724259","https://openalex.org/W1805381866","https://openalex.org/W1912930600","https://openalex.org/W1978810688","https://openalex.org/W1991061778","https://openalex.org/W1993204543","https://openalex.org/W1998752961","https://openalex.org/W2009884382","https://openalex.org/W2011285532","https://openalex.org/W2022963516","https://openalex.org/W2025604712","https://openalex.org/W2028680761","https://openalex.org/W2036854337","https://openalex.org/W2039707205","https://openalex.org/W2052337595","https://openalex.org/W2058534741","https://openalex.org/W2059518219","https://openalex.org/W2065831380","https://openalex.org/W2074630359","https://openalex.org/W2082849992","https://openalex.org/W2088123313","https://openalex.org/W2097715593","https://openalex.org/W2133272838","https://openalex.org/W2333289369","https://openalex.org/W2572075230","https://openalex.org/W4239114676","https://openalex.org/W4247375400","https://openalex.org/W4253937035","https://openalex.org/W4285719527","https://openalex.org/W4298060601","https://openalex.org/W4300846967"],"related_works":["https://openalex.org/W151444058","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2169386430","https://openalex.org/W2548490812","https://openalex.org/W2887215440","https://openalex.org/W1513480254","https://openalex.org/W3034882149","https://openalex.org/W2047352485","https://openalex.org/W1970590191"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,55],"propose":[4],"a":[5,28],"new":[6],"Galerkin":[7,65],"spectral":[8,42,66],"element":[9,43,67],"method":[10],"for":[11],"one-dimensional":[12],"fourth-order":[13,51],"boundary":[14,52],"value":[15,53],"problems.":[16],"We":[17],"first":[18],"introduce":[19],"some":[20],"quasi-orthogonal":[21],"approximations":[22],"in":[23,40,74],"one":[24],"dimension,":[25],"and":[26,59,82],"establish":[27,56],"series":[29],"of":[30,63],"results":[31,48,77],"on":[32],"these":[33,47],"approximations,":[34],"which":[35],"serve":[36],"as":[37],"powerful":[38],"tools":[39],"the":[41,50,64,84],"method.":[44,68],"By":[45],"applying":[46],"to":[49],"problems,":[54],"sharp":[57],"H2":[58],"L2":[60],"error":[61],"bounds":[62],"The":[69],"efficient":[70],"algorithm":[71],"is":[72],"implemented":[73],"detail.":[75],"Numerical":[76],"demonstrate":[78],"its":[79],"high":[80],"accuracy,":[81],"confirm":[83],"theoretical":[85],"analysis":[86],"well.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
