{"id":"https://openalex.org/W1977399978","doi":"https://doi.org/10.1137/040608490","title":"Convergence Analysis of a Multiscale Finite Element Method for Singularly Perturbed Problems","display_name":"Convergence Analysis of a Multiscale Finite Element Method for Singularly Perturbed Problems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1977399978","doi":"https://doi.org/10.1137/040608490","mag":"1977399978"},"language":"en","primary_location":{"id":"doi:10.1137/040608490","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040608490","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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/A5108440518","display_name":"Leopoldo P. Franca","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leopoldo P. Franca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069256499","display_name":"Alexandre L. Madureira","orcid":"https://orcid.org/0000-0002-8493-4905"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre L. Madureira","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053874836","display_name":"Lutz Tobiska","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lutz Tobiska","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059362886","display_name":"Fr\u00e9d\u00e9ric Valentin","orcid":"https://orcid.org/0000-0002-5056-7529"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Valentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3613,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.88249712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"3","first_page":"839","last_page":"866"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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":0.9994999766349792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7749576568603516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6788910031318665},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.602080762386322},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5858936309814453},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.578738808631897},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5342884063720703},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.532819926738739},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5314207077026367},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.5132694244384766},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.48243722319602966},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4652681350708008},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.41789448261260986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40605512261390686},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1403839886188507}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7749576568603516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6788910031318665},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.602080762386322},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5858936309814453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.578738808631897},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5342884063720703},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.532819926738739},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5314207077026367},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.5132694244384766},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.48243722319602966},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4652681350708008},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.41789448261260986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40605512261390686},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1403839886188507},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/040608490","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040608490","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.553.2479","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.553.2479","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lncc.br/~valentin/docs/FraFraTobVal05.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W53139918","https://openalex.org/W79873316","https://openalex.org/W124532162","https://openalex.org/W248929352","https://openalex.org/W1535281435","https://openalex.org/W1550521431","https://openalex.org/W1964846831","https://openalex.org/W1966480196","https://openalex.org/W1971988228","https://openalex.org/W1976509668","https://openalex.org/W1987394193","https://openalex.org/W1995044934","https://openalex.org/W1995404822","https://openalex.org/W2009628646","https://openalex.org/W2009852560","https://openalex.org/W2009933241","https://openalex.org/W2011078493","https://openalex.org/W2014983931","https://openalex.org/W2020275136","https://openalex.org/W2023502036","https://openalex.org/W2025068220","https://openalex.org/W2027768313","https://openalex.org/W2029918260","https://openalex.org/W2041523977","https://openalex.org/W2053342859","https://openalex.org/W2056971886","https://openalex.org/W2062618977","https://openalex.org/W2073897969","https://openalex.org/W2074772185","https://openalex.org/W2083183178","https://openalex.org/W2116132944","https://openalex.org/W2127473876","https://openalex.org/W2155879256","https://openalex.org/W2157721313","https://openalex.org/W2164555111","https://openalex.org/W2505585705","https://openalex.org/W2745073160","https://openalex.org/W4236548481"],"related_works":["https://openalex.org/W4288262055","https://openalex.org/W2967076701","https://openalex.org/W2990320605","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2927373829","https://openalex.org/W4321472236","https://openalex.org/W4234704706","https://openalex.org/W2073705841","https://openalex.org/W4293558596"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,85],"perform":[4,77],"an":[5,89],"error":[6],"analysis":[7,79],"for":[8,14,62],"a":[9,20],"multiscale":[10],"finite":[11,30],"element":[12,31,53],"method":[13,21,71,104],"singularly":[15],"perturbed":[16],"reaction-diffusion":[17],"equations.":[18],"Such":[19],"is":[22,72,105],"based":[23],"on":[24,51,111],"enriching":[25],"the":[26,38,42,60,63,95,102],"usual":[27],"piecewise":[28],"linear":[29,56],"trial":[32],"spaces":[33],"with":[34,92],"local":[35],"solutions":[36,109],"of":[37,73],"original":[39],"problem,":[40],"but":[41],"approach":[43],"does":[44],"not":[45],"require":[46],"these":[47],"functions":[48,65],"to":[49,94,107],"vanish":[50],"each":[52],"edge.":[54],"Piecewise":[55],"plus":[57],"bubbles":[58],"are":[59],"choice":[61],"test":[64],"allowing":[66],"static":[67],"condensation;":[68],"thus":[69],"our":[70],"Petrov--Galerkin":[74],"type.":[75],"We":[76],"convergence":[78,87],"in":[80,88],"different":[81],"asymptotic":[82],"regimes,":[83],"and":[84],"show":[86,100],"appropriate":[90],"norm":[91],"respect":[93],"small":[96],"parameter.":[97],"Numerical":[98],"results":[99],"that":[101],"new":[103],"able":[106],"compute":[108],"even":[110],"coarse":[112],"meshes.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
