{"id":"https://openalex.org/W2064991465","doi":"https://doi.org/10.1090/s0025-5718-96-00746-6","title":"Two-level additive Schwarz preconditioners for nonconforming finite element methods","display_name":"Two-level additive Schwarz preconditioners for nonconforming finite element methods","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2064991465","doi":"https://doi.org/10.1090/s0025-5718-96-00746-6","mag":"2064991465"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00746-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00746-6","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00746-6/S0025-5718-96-00746-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00746-6/S0025-5718-96-00746-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061146602","display_name":"Susanne C. Brenner","orcid":"https://orcid.org/0000-0001-8330-5667"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]},{"id":"https://openalex.org/I16944753","display_name":"Clarkson University","ror":"https://ror.org/03rwgpn18","country_code":"US","type":"education","lineage":["https://openalex.org/I16944753"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Susanne Brenner","raw_affiliation_strings":["Department of Mathematics and Computer Science, Clarkson University, Potsdam, New York 13699-5815","Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Clarkson University, Potsdam, New York 13699-5815","institution_ids":["https://openalex.org/I16944753"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061146602"],"corresponding_institution_ids":["https://openalex.org/I155781252","https://openalex.org/I16944753"],"apc_list":null,"apc_paid":null,"fwci":7.5621,"has_fulltext":true,"cited_by_count":136,"citation_normalized_percentile":{"value":0.97704025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"65","issue":"215","first_page":"897","last_page":"921"},"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":0.9998999834060669,"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":0.9998999834060669,"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/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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9965000152587891,"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":0.9073513746261597},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.852339506149292},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.785000205039978},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7572160959243774},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.5973193645477295},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5044196844100952},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5024638175964355},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4506049156188965},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.44882023334503174},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.443948358297348},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4202679991722107},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3839108347892761},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.37928342819213867}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9073513746261597},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.852339506149292},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.785000205039978},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7572160959243774},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.5973193645477295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5044196844100952},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5024638175964355},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4506049156188965},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.44882023334503174},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.443948358297348},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4202679991722107},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3839108347892761},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.37928342819213867},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-96-00746-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00746-6","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00746-6/S0025-5718-96-00746-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1199","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/200","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00746-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00746-6","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00746-6/S0025-5718-96-00746-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2064991465.pdf","grobid_xml":"https://content.openalex.org/works/W2064991465.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W20824204","https://openalex.org/W206256087","https://openalex.org/W618110921","https://openalex.org/W1492326914","https://openalex.org/W1540854488","https://openalex.org/W1585767079","https://openalex.org/W1977522442","https://openalex.org/W1995913204","https://openalex.org/W2017085690","https://openalex.org/W2031712828","https://openalex.org/W2041523977","https://openalex.org/W2042732056","https://openalex.org/W2054781196","https://openalex.org/W2592623476","https://openalex.org/W4249945978","https://openalex.org/W4254349521","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2026475824","https://openalex.org/W2493580937"],"abstract_inverted_index":{"Two-level":[0],"additive":[1],"Schwarz":[2],"preconditioners":[3],"are":[4,52],"developed":[5],"for":[6],"the":[7,23,29,33,41,49,62,67],"nonconforming":[8,35],"P1":[9,36],"finite":[10,25,37],"element":[11,26,38],"approximation":[12,27,39],"of":[13,28,40,48,58,64,69],"scalar":[14],"second-order":[15],"symmetric":[16],"positive":[17],"definite":[18],"elliptic":[19],"boundary":[20],"value":[21],"problems,":[22],"Morley":[24],"biharmonic":[30],"equation,":[31],"and":[32,61],"divergence-free":[34],"stationary":[42],"Stokes":[43],"equations.":[44],"The":[45],"condition":[46],"numbers":[47],"preconditioned":[50],"systems":[51],"shown":[53],"to":[54],"be":[55],"bounded":[56],"independent":[57],"mesh":[59],"sizes":[60],"number":[63],"subdomains":[65],"in":[66],"case":[68],"generous":[70],"overlap.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}