{"id":"https://openalex.org/W2192056604","doi":"https://doi.org/10.1023/a:1012284322811","title":"Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems","display_name":"Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems","publication_year":2001,"publication_date":"2001-05-01","ids":{"openalex":"https://openalex.org/W2192056604","doi":"https://doi.org/10.1023/a:1012284322811","mag":"2192056604"},"language":"en","primary_location":{"id":"doi:10.1023/a:1012284322811","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1012284322811","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational 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/A5014166483","display_name":"Jinchao Xu","orcid":"https://orcid.org/0000-0002-1530-6913"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jinchao Xu","raw_affiliation_strings":["Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, USA","Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113202217","display_name":"Aihui Zhou","orcid":null},"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Aihui Zhou","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China","Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014166483","https://openalex.org/A5113202217"],"corresponding_institution_ids":["https://openalex.org/I130769515","https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.874,"has_fulltext":false,"cited_by_count":126,"citation_normalized_percentile":{"value":0.8533371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"293","last_page":"327"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9980999827384949,"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/discretization","display_name":"Discretization","score":0.8061028718948364},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7570163607597351},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7493810653686523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.660800039768219},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6178353428840637},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.534959614276886},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.520125687122345},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.5028561949729919},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5019078254699707},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.4875485301017761},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4179531931877136},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41608676314353943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30766814947128296},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29735398292541504},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2517312169075012}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8061028718948364},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7570163607597351},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7493810653686523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.660800039768219},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6178353428840637},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.534959614276886},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.520125687122345},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.5028561949729919},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5019078254699707},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.4875485301017761},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4179531931877136},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41608676314353943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30766814947128296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29735398292541504},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2517312169075012},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1023/a:1012284322811","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1012284322811","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310419","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W94976795","https://openalex.org/W228399867","https://openalex.org/W604177120","https://openalex.org/W1586623601","https://openalex.org/W1593553932","https://openalex.org/W1595515622","https://openalex.org/W1970850839","https://openalex.org/W1975664127","https://openalex.org/W1980455776","https://openalex.org/W1982458994","https://openalex.org/W1986438698","https://openalex.org/W1989343938","https://openalex.org/W1989594010","https://openalex.org/W1989819667","https://openalex.org/W1994336408","https://openalex.org/W2001012793","https://openalex.org/W2003836934","https://openalex.org/W2007751122","https://openalex.org/W2008086872","https://openalex.org/W2012229545","https://openalex.org/W2017085690","https://openalex.org/W2017786109","https://openalex.org/W2019589016","https://openalex.org/W2020571215","https://openalex.org/W2024418403","https://openalex.org/W2027985026","https://openalex.org/W2031387765","https://openalex.org/W2033653234","https://openalex.org/W2038626747","https://openalex.org/W2039877000","https://openalex.org/W2041568728","https://openalex.org/W2042248875","https://openalex.org/W2050361884","https://openalex.org/W2056027508","https://openalex.org/W2058525241","https://openalex.org/W2061937382","https://openalex.org/W2065874602","https://openalex.org/W2066927514","https://openalex.org/W2067734800","https://openalex.org/W2069048447","https://openalex.org/W2069961480","https://openalex.org/W2071036364","https://openalex.org/W2076458295","https://openalex.org/W2082051696","https://openalex.org/W2085422562","https://openalex.org/W2086943675","https://openalex.org/W2104126767","https://openalex.org/W2148639620","https://openalex.org/W2151317657","https://openalex.org/W2153127767","https://openalex.org/W2163694039","https://openalex.org/W2317987601","https://openalex.org/W2482440048","https://openalex.org/W4230055019","https://openalex.org/W4240003552","https://openalex.org/W4250470418","https://openalex.org/W4252219741","https://openalex.org/W4255110285","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W37066597","https://openalex.org/W25733641","https://openalex.org/W1977553163","https://openalex.org/W1993570899","https://openalex.org/W1555094802","https://openalex.org/W4230197975","https://openalex.org/W188298612","https://openalex.org/W3128822846","https://openalex.org/W2046814020","https://openalex.org/W2028070877"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}
