{"id":"https://openalex.org/W2127722022","doi":"https://doi.org/10.1137/110832999","title":"Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods","display_name":"Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2127722022","doi":"https://doi.org/10.1137/110832999","mag":"2127722022"},"language":"en","primary_location":{"id":"doi:10.1137/110832999","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832999","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/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. M. Melenk","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5018841476","display_name":"Barbara Wohlmuth","orcid":"https://orcid.org/0000-0001-6908-6015"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Wohlmuth","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058356670"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1145,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94095981,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"4","first_page":"2064","last_page":"2087"},"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":0.9994999766349792,"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":0.9975000023841858,"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/mathematics","display_name":"Mathematics","score":0.8785922527313232},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8161065578460693},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6331453323364258},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.5769996643066406},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5667906999588013},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5134493112564087},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4818105101585388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47642239928245544},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4502909183502197},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4395908713340759},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4311399459838867},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33509498834609985},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23839882016181946},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23100462555885315}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8785922527313232},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8161065578460693},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6331453323364258},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.5769996643066406},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5667906999588013},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5134493112564087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4818105101585388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47642239928245544},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4502909183502197},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4395908713340759},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4311399459838867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33509498834609985},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23839882016181946},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23100462555885315},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":2,"locations":[{"id":"doi:10.1137/110832999","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832999","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:mediatum.ub.tum.de:node/1685060","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1685060","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":25,"referenced_works":["https://openalex.org/W94976795","https://openalex.org/W266838890","https://openalex.org/W574578250","https://openalex.org/W1533889494","https://openalex.org/W1545082185","https://openalex.org/W1547166419","https://openalex.org/W1593038947","https://openalex.org/W1595515622","https://openalex.org/W1595782612","https://openalex.org/W1852082788","https://openalex.org/W1866311589","https://openalex.org/W1979157957","https://openalex.org/W1991647816","https://openalex.org/W1995745706","https://openalex.org/W2021965139","https://openalex.org/W2050222014","https://openalex.org/W2058398001","https://openalex.org/W2072097343","https://openalex.org/W2079423956","https://openalex.org/W2137810984","https://openalex.org/W2159415209","https://openalex.org/W2225162326","https://openalex.org/W2251490743","https://openalex.org/W2487882368","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W3127021889","https://openalex.org/W4308799551","https://openalex.org/W2390298288","https://openalex.org/W79911096"],"abstract_inverted_index":{"We":[0,30],"show":[1],"quasi-optimal":[2],"a":[3,59,101],"priori":[4,60,102],"convergence":[5],"results":[6],"in":[7,24,36,99,125],"the":[8,13,25,33,37,47,63,69,100,105,116,122],"$L^2$-":[9],"and":[10,49,55,84],"$H^{-1/2}$-norm":[11],"for":[12,45,62,85,104,121],"approximation":[14],"of":[15,78,96,118,127],"surface":[16],"based":[17,114],"Lagrange":[18],"multipliers":[19],"such":[20],"as":[21],"those":[22],"employed":[23],"mortar":[26],"finite":[27],"element":[28],"method.":[29],"improve":[31],"on":[32,115],"estimates":[34,44,61,120],"obtained":[35,53],"standard":[38],"saddle":[39],"point":[40],"theory,":[41],"where":[42],"error":[43],"both":[46],"primal":[48,123],"dual":[50,64,106],"variables":[51],"are":[52,66],"simultaneously":[54],"thus":[56],"only":[57],"suboptimal":[58],"variable":[65,107,124],"reached.":[67],"For":[68],"lowest":[70],"order":[71,87],"case,":[72],"i.e.,":[73,89],"$k=1$,":[74],"an":[75,93],"additional":[76,94],"factor":[77,95],"$\\sqrt{h}":[79],"|":[80],"\\ln":[81],"h":[82],"|$":[83],"higher":[86],"cases,":[88],"$k":[90],">":[91],"1$,":[92],"$":[97],"\\sqrt{h}$":[98],"bound":[103],"can":[108],"be":[109],"recovered.":[110],"The":[111],"proof":[112],"is":[113],"use":[117],"new":[119],"strips":[126],"width":[128],"$O(h)$":[129],"near":[130],"these":[131],"surfaces.":[132]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
