{"id":"https://openalex.org/W2019839867","doi":"https://doi.org/10.1007/s00211-005-0625-2","title":"Additive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients","display_name":"Additive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients","publication_year":2005,"publication_date":"2005-07-27","ids":{"openalex":"https://openalex.org/W2019839867","doi":"https://doi.org/10.1007/s00211-005-0625-2","mag":"2019839867"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-005-0625-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-005-0625-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5102366721","display_name":"Talal Rahman","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Talal Rahman","raw_affiliation_strings":["Bergen Center for Computational Science, University of Bergen, Thorm\u00f8hlensgt. 55, 5008, Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bergen Center for Computational Science, University of Bergen, Thorm\u00f8hlensgt. 55, 5008, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":["LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105206538","display_name":"Ronald H. W. Hoppe","orcid":"https://orcid.org/0000-0003-2287-6102"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]},{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Ronald Hoppe","raw_affiliation_strings":["Department of Mathematics, University of Houston, Calhoun Street, Houston, TX77204-3008, USA","Institute of Mathematics, University of Augsburg, Universit\u00e4tsstr. 14, 86159, Augsburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Calhoun Street, Houston, TX77204-3008, USA","institution_ids":["https://openalex.org/I44461941"]},{"raw_affiliation_string":"Institute of Mathematics, University of Augsburg, Universit\u00e4tsstr. 14, 86159, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102366721"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.8532,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.83487093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"101","issue":"3","first_page":"551","last_page":"572"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980999827384949,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9975000023841858,"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/discretization","display_name":"Discretization","score":0.8530788421630859},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.8462815284729004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8390113115310669},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.681890606880188},{"id":"https://openalex.org/keywords/mortar-methods","display_name":"Mortar methods","score":0.6464451551437378},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6098981499671936},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5143646001815796},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4962692856788635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.469463974237442},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4626610577106476},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.4529529809951782},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4487902522087097},{"id":"https://openalex.org/keywords/mortar","display_name":"Mortar","score":0.4158249795436859},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.41026103496551514},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.06978678703308105},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.062296926975250244}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8530788421630859},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.8462815284729004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8390113115310669},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.681890606880188},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.6464451551437378},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6098981499671936},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5143646001815796},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4962692856788635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.469463974237442},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4626610577106476},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.4529529809951782},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4487902522087097},{"id":"https://openalex.org/C130767629","wikidata":"https://www.wikidata.org/wiki/Q7905205","display_name":"Mortar","level":2,"score":0.4158249795436859},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.41026103496551514},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.06978678703308105},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.062296926975250244},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-005-0625-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-005-0625-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.144.4245","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.4245","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ii.uib.no/~talal/html/papers/pdf/Numerische_Rahman_Xu_Hoppe_ASM_CR_Mortar.pdf","raw_type":"text"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:34944","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/34944","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:50292","is_oa":false,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-502927","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"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/W904235","https://openalex.org/W1512418819","https://openalex.org/W1513884443","https://openalex.org/W1530566973","https://openalex.org/W1540708723","https://openalex.org/W1542243431","https://openalex.org/W1547166419","https://openalex.org/W1570966844","https://openalex.org/W1795839839","https://openalex.org/W1974155734","https://openalex.org/W2010427465","https://openalex.org/W2015280312","https://openalex.org/W2017437995","https://openalex.org/W2017703114","https://openalex.org/W2019962492","https://openalex.org/W2020854958","https://openalex.org/W2021257096","https://openalex.org/W2027019002","https://openalex.org/W2031182879","https://openalex.org/W2041523977","https://openalex.org/W2042248875","https://openalex.org/W2045656285","https://openalex.org/W2050222014","https://openalex.org/W2064991465","https://openalex.org/W2092565530","https://openalex.org/W2105555500","https://openalex.org/W2326261353","https://openalex.org/W2491027544","https://openalex.org/W2557433803","https://openalex.org/W2798909945","https://openalex.org/W4206453220","https://openalex.org/W4210300254","https://openalex.org/W4241403127","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W4241403127","https://openalex.org/W4229577910","https://openalex.org/W596860038","https://openalex.org/W2153233687","https://openalex.org/W3157524857","https://openalex.org/W4288293110","https://openalex.org/W2955329227"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}