{"id":"https://openalex.org/W4200566441","doi":"https://doi.org/10.1007/s10915-021-01696-5","title":"A Posteriori Error Estimates of Spectral Approximations for Second Order Partial Differential Equations in Spherical Geometries","display_name":"A Posteriori Error Estimates of Spectral Approximations for Second Order Partial Differential Equations in Spherical Geometries","publication_year":2021,"publication_date":"2021-12-18","ids":{"openalex":"https://openalex.org/W4200566441","doi":"https://doi.org/10.1007/s10915-021-01696-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01696-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01696-5","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/A5046354456","display_name":"Jianwei Zhou","orcid":"https://orcid.org/0000-0002-1288-5905"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianwei Zhou","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China","School of Mathematics and Statistics, Linyi University, Shandong, 276005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Linyi University, Shandong, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100637657","display_name":"Huiyuan Li","orcid":"https://orcid.org/0000-0002-6326-9926"},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiyuan Li","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China","Institute of Software, Chinese Academy of Science, Beijing, 100190, China"],"raw_orcid":"https://orcid.org/0000-0002-6326-9926","affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Institute of Software, Chinese Academy of Science, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210128818"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073157317","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0009-0000-8778-7149"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]},{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing, 100193, China","Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing, 100193, China","institution_ids":["https://openalex.org/I4210139958"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.0625,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.94329091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"90","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8885669112205505},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.677021861076355},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5717588663101196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5375369191169739},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.49080929160118103},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.4477984309196472},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4297848343849182},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4199303984642029},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4128863513469696},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21936318278312683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8885669112205505},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.677021861076355},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5717588663101196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5375369191169739},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.49080929160118103},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.4477984309196472},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4297848343849182},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4199303984642029},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4128863513469696},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21936318278312683},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-021-01696-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01696-5","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":[{"id":"https://openalex.org/G3594134181","display_name":null,"funder_award_id":"11926355","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4646362747","display_name":"\u7535\u78c1\u573a\u65b9\u7a0b\u53ca\u5176\u7279\u5f81\u503c\u95ee\u9898\u9ad8\u6548\u9ad8\u7cbe\u5ea6\u6570\u503c\u65b9\u6cd5","funder_award_id":"11871092","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4801177068","display_name":null,"funder_award_id":"2019KJI003","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5403852501","display_name":null,"funder_award_id":"ZR2019YQ05","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5569235300","display_name":null,"funder_award_id":"NSAF U1930402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G674121926","display_name":null,"funder_award_id":"2018YFB0204404","funder_id":"https://openalex.org/F4320335774","funder_display_name":"Key Technologies Research and Development Program"},{"id":"https://openalex.org/G6923539676","display_name":null,"funder_award_id":"11971016","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7313997272","display_name":null,"funder_award_id":"2017T100030","funder_id":"https://openalex.org/F4320335443","funder_display_name":"Postdoctoral Research Foundation of China"},{"id":"https://openalex.org/G7654190659","display_name":null,"funder_award_id":"2017M610751","funder_id":"https://openalex.org/F4320335443","funder_display_name":"Postdoctoral Research Foundation of China"},{"id":"https://openalex.org/G8148267054","display_name":null,"funder_award_id":"11871145","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"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320335443","display_name":"Postdoctoral Research Foundation of China","ror":null},{"id":"https://openalex.org/F4320335774","display_name":"Key Technologies Research and Development Program","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W321261355","https://openalex.org/W567568486","https://openalex.org/W1533889494","https://openalex.org/W1607663648","https://openalex.org/W1805381866","https://openalex.org/W1833891341","https://openalex.org/W1912930600","https://openalex.org/W1994336408","https://openalex.org/W1995404822","https://openalex.org/W2000811891","https://openalex.org/W2001413153","https://openalex.org/W2001849333","https://openalex.org/W2021572240","https://openalex.org/W2022982334","https://openalex.org/W2024409565","https://openalex.org/W2030028670","https://openalex.org/W2036490127","https://openalex.org/W2044892973","https://openalex.org/W2045354979","https://openalex.org/W2059030063","https://openalex.org/W2061528771","https://openalex.org/W2069242965","https://openalex.org/W2071289502","https://openalex.org/W2071637142","https://openalex.org/W2072341301","https://openalex.org/W2122461891","https://openalex.org/W2122602456","https://openalex.org/W2130038269","https://openalex.org/W2130655033","https://openalex.org/W2155395549","https://openalex.org/W2161962797","https://openalex.org/W2166590326","https://openalex.org/W2319345516","https://openalex.org/W2339152380","https://openalex.org/W3152171430","https://openalex.org/W4211228115","https://openalex.org/W4231397690","https://openalex.org/W4237634459","https://openalex.org/W4239114676","https://openalex.org/W4242464733","https://openalex.org/W4243237667","https://openalex.org/W4247375400","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2379042074","https://openalex.org/W4287880334","https://openalex.org/W4300097986","https://openalex.org/W2153939185","https://openalex.org/W2011653182","https://openalex.org/W2540706492","https://openalex.org/W167165788","https://openalex.org/W2589923138","https://openalex.org/W2028474363","https://openalex.org/W4211187909"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
