{"id":"https://openalex.org/W2094840682","doi":"https://doi.org/10.1007/s10915-015-9983-9","title":"An $$h$$ h \u2013 $$p$$ p Version of the Continuous Petrov\u2013Galerkin Finite Element Method for Nonlinear Volterra Integro-Differential Equations","display_name":"An $$h$$ h \u2013 $$p$$ p Version of the Continuous Petrov\u2013Galerkin Finite Element Method for Nonlinear Volterra Integro-Differential Equations","publication_year":2015,"publication_date":"2015-01-10","ids":{"openalex":"https://openalex.org/W2094840682","doi":"https://doi.org/10.1007/s10915-015-9983-9","mag":"2094840682"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-015-9983-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-015-9983-9","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/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"]},{"id":"https://openalex.org/I4210160248","display_name":"Shanghai Universities E-Institute for Chemical Biology","ror":"https://ror.org/03h7eyw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210160248"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lijun Yi","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China","Division of Computational Science, E-institute of Shanghai Universities, Shanghai, 200234, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China","institution_ids":["https://openalex.org/I21945476"]},{"raw_affiliation_string":"Division of Computational Science, E-institute of Shanghai Universities, Shanghai, 200234, China","institution_ids":["https://openalex.org/I4210160248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084338992"],"corresponding_institution_ids":["https://openalex.org/I21945476","https://openalex.org/I4210160248"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.5193,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.92743675,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"2","first_page":"715","last_page":"734"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9080942869186401},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.7284523844718933},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.6667866706848145},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.63669753074646},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6243364810943604},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6045594215393066},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5846526622772217},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5453590154647827},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5371222496032715},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4766702950000763},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4447086453437805},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.41348153352737427},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2461778223514557}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9080942869186401},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.7284523844718933},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.6667866706848145},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.63669753074646},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6243364810943604},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6045594215393066},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5846526622772217},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5453590154647827},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5371222496032715},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4766702950000763},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4447086453437805},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.41348153352737427},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2461778223514557},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-015-9983-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-015-9983-9","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W191236717","https://openalex.org/W1567668233","https://openalex.org/W1978612347","https://openalex.org/W1979551969","https://openalex.org/W1986006981","https://openalex.org/W1986683394","https://openalex.org/W1988932741","https://openalex.org/W1994678449","https://openalex.org/W1996037589","https://openalex.org/W1996143385","https://openalex.org/W2012062138","https://openalex.org/W2014617375","https://openalex.org/W2017571276","https://openalex.org/W2022694169","https://openalex.org/W2028224531","https://openalex.org/W2031613888","https://openalex.org/W2031625690","https://openalex.org/W2041588624","https://openalex.org/W2044385163","https://openalex.org/W2047136919","https://openalex.org/W2050380784","https://openalex.org/W2082693172","https://openalex.org/W2084872583","https://openalex.org/W2086119896","https://openalex.org/W2089266075","https://openalex.org/W2151276461","https://openalex.org/W2171286355","https://openalex.org/W2404351776","https://openalex.org/W2556715742","https://openalex.org/W3120038842","https://openalex.org/W3121012624"],"related_works":["https://openalex.org/W2394496373","https://openalex.org/W2080756705","https://openalex.org/W2366365323","https://openalex.org/W2613898712","https://openalex.org/W4289285311","https://openalex.org/W220460885","https://openalex.org/W2034350085","https://openalex.org/W137108797","https://openalex.org/W3158373710","https://openalex.org/W2010894337"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}