{"id":"https://openalex.org/W2075108106","doi":"https://doi.org/10.1137/s0036142998335431","title":"A Multigrid Algorithm for the Mortar Finite Element Method","display_name":"A Multigrid Algorithm for the Mortar Finite Element Method","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2075108106","doi":"https://doi.org/10.1137/s0036142998335431","mag":"2075108106"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998335431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335431","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5019658783","display_name":"Dietrich Braess","orcid":"https://orcid.org/0009-0007-7232-0299"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dietrich Braess","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106691969","display_name":"Wolfgang Dahmen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wolfgang Dahmen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008644618","display_name":"Christian Wieners","orcid":"https://orcid.org/0000-0001-6242-6777"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christian Wieners","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.7183,"has_fulltext":false,"cited_by_count":116,"citation_normalized_percentile":{"value":0.99632691,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"1","first_page":"48","last_page":"69"},"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":0.9983999729156494,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/multigrid-method","display_name":"Multigrid method","score":0.8288342356681824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.731913685798645},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.691757321357727},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6511564254760742},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5448406338691711},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5206417441368103},{"id":"https://openalex.org/keywords/mortar-methods","display_name":"Mortar methods","score":0.4437550902366638},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4322810471057892},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40723878145217896},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.38114869594573975},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.33747345209121704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2636479139328003}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8288342356681824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.731913685798645},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.691757321357727},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6511564254760742},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5448406338691711},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5206417441368103},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.4437550902366638},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4322810471057892},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40723878145217896},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.38114869594573975},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.33747345209121704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2636479139328003},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0036142998335431","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335431","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.8956","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.8956","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cox.iwr.uni-heidelberg.de/~wieners/publications/braessdahmenwieners.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.29.6316","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6316","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://www.igpm.rwth-aachen.de/pub/dahmen/bdw_siam.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.1591","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1591","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ntu.edu.tw/~yccen/wavelet/dahmen/siam_last.ps.Z","raw_type":"text"},{"id":"pmh:oai:publications.rwth-aachen.de:161468","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/161468","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on numerical analysis 37(1), 48-69 (1999). doi:10.1137/S0036142998335431","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:publications.rwth-aachen.de:47115","is_oa":false,"landing_page_url":"http://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-007932%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aachen : Institut f\u00fcr Geometrie und Praktische Mathematik, Bericht / Institut f\u00fcr Geometrie und Praktische Mathematik, RWTH Aachen 153, (1998).","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W904235","https://openalex.org/W1512418819","https://openalex.org/W1545082185","https://openalex.org/W1586623601","https://openalex.org/W1597209545","https://openalex.org/W1991647816","https://openalex.org/W1992542433","https://openalex.org/W2017437995","https://openalex.org/W2019779194","https://openalex.org/W2021921526","https://openalex.org/W2037067761","https://openalex.org/W2037836476","https://openalex.org/W2041563881","https://openalex.org/W2051588145","https://openalex.org/W2088959663","https://openalex.org/W2094281210","https://openalex.org/W2127981460","https://openalex.org/W2199169705","https://openalex.org/W2402147915","https://openalex.org/W2464303547","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2501988474","https://openalex.org/W4289744189","https://openalex.org/W2883343539","https://openalex.org/W2021837978","https://openalex.org/W1973136543","https://openalex.org/W2001529763","https://openalex.org/W2295047789","https://openalex.org/W240948612","https://openalex.org/W1527096857","https://openalex.org/W2119544289"],"abstract_inverted_index":{"The":[0],"objective":[1],"of":[2,16,25,50,60,74,131,139,155],"this":[3],"paper":[4],"is":[5,91,124],"to":[6,34,45,114,126],"develop":[7],"and":[8,44,84,148,152],"analyze":[9],"a":[10,96,106,121],"multigrid":[11,102,117],"algorithm":[12],"for":[13,39,79,94,100],"the":[14,20,36,40,47,51,57,61,72,75,80,92,127,140,145,150,153,156,164],"system":[15,130],"equations":[17],"arising":[18],"from":[19],"mortar":[21,62],"finite":[22,63],"element":[23,64],"discretization":[24],"second":[26],"order":[27,33],"elliptic":[28],"boundary":[29],"value":[30],"problems.":[31],"In":[32,109],"establish":[35],"inf-sup":[37],"condition":[38,78],"saddle":[41],"point":[42],"formulation":[43],"motivate":[46],"subsequent":[48],"treatment":[49],"discretizations,":[52],"we":[53,70,111],"first":[54],"revisit":[55],"briefly":[56],"theoretical":[58,146],"concept":[59],"method.":[65],"Employing":[66],"suitable":[67,97],"mesh-dependent":[68],"norms":[69],"verify":[71,115],"validity":[73],"Ladyzhenskaya--Babuska--Brezzi":[76],"(LBB)":[77],"resulting":[81],"mixed":[82],"method":[83,157],"prove":[85],"an":[86],"L2":[87],"error":[88],"estimate.":[89],"This":[90],"key":[93],"establishing":[95],"approximation":[98],"property":[99],"our":[101],"convergence":[103],"proof":[104],"via":[105],"duality":[107],"argument.":[108],"fact,":[110],"are":[112],"able":[113],"optimal":[116],"efficiency":[118,151],"based":[119],"on":[120],"smoother":[122],"which":[123,143],"applied":[125],"whole":[128],"coupled":[129],"equations.":[132],"We":[133],"conclude":[134],"with":[135],"several":[136],"numerical":[137],"tests":[138],"proposed":[141],"scheme":[142],"confirm":[144],"results":[147],"show":[149],"robustness":[154],"even":[158],"in":[159],"situations":[160],"not":[161],"covered":[162],"by":[163],"theory.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
