{"id":"https://openalex.org/W3034362099","doi":"https://doi.org/10.1515/cmam-2021-0030","title":"Error Estimation and Adaptivity for Differential Equations with Multiple Scales in Time","display_name":"Error Estimation and Adaptivity for Differential Equations with Multiple Scales in Time","publication_year":2021,"publication_date":"2021-04-20","ids":{"openalex":"https://openalex.org/W3034362099","doi":"https://doi.org/10.1515/cmam-2021-0030","mag":"3034362099"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2021-0030","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2021-0030","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.05420","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017320967","display_name":"Leopold Lautsch","orcid":"https://orcid.org/0009-0000-4134-3163"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Leopold Lautsch","raw_affiliation_strings":["Otto-von-Guericke Universit\u00e4t Magdeburg , Magdeburg , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Otto-von-Guericke Universit\u00e4t Magdeburg , Magdeburg , Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060011936","display_name":"Thomas Richter","orcid":"https://orcid.org/0000-0003-0206-3606"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas Richter","raw_affiliation_strings":["Otto-von-Guericke Universit\u00e4t Magdeburg , Magdeburg , Germany"],"raw_orcid":"https://orcid.org/0000-0003-0206-3606","affiliations":[{"raw_affiliation_string":"Otto-von-Guericke Universit\u00e4t Magdeburg , Magdeburg , Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060011936"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":null,"apc_paid":null,"fwci":0.7922,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74135453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"21","issue":"4","first_page":"841","last_page":"861"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/estimator","display_name":"Estimator","score":0.7927970290184021},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6713895797729492},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6566171646118164},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.6040789484977722},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5893946886062622},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5316126346588135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5029603838920593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45483511686325073},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43591466546058655},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40424466133117676},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38925811648368835},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3827870190143585},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10640135407447815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10206276178359985}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7927970290184021},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6713895797729492},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6566171646118164},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.6040789484977722},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5893946886062622},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5316126346588135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5029603838920593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45483511686325073},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43591466546058655},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40424466133117676},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38925811648368835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3827870190143585},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10640135407447815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10206276178359985},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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":2,"locations":[{"id":"doi:10.1515/cmam-2021-0030","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2021-0030","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.05420","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05420","pdf_url":"https://arxiv.org/pdf/2006.05420","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.05420","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05420","pdf_url":"https://arxiv.org/pdf/2006.05420","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3150829247","display_name":"GRK 2297: Mathematische Komplexit\u00e4tsreduktion","funder_award_id":"314838170","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5177846589","display_name":null,"funder_award_id":"05M16NMA","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G7669840397","display_name":"Simulation und Analysis f\u00fcr zeitliche Mehrskalenprobleme mit partiellen Differentialgleichungen","funder_award_id":"411046898","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W377201621","https://openalex.org/W650857255","https://openalex.org/W1553150814","https://openalex.org/W1966426357","https://openalex.org/W1971947347","https://openalex.org/W1990157709","https://openalex.org/W1998967184","https://openalex.org/W2008736432","https://openalex.org/W2011247691","https://openalex.org/W2016728159","https://openalex.org/W2045981428","https://openalex.org/W2071362850","https://openalex.org/W2082621526","https://openalex.org/W2090807663","https://openalex.org/W2133147107","https://openalex.org/W2138940269","https://openalex.org/W2148639620","https://openalex.org/W2418402168","https://openalex.org/W2505515853","https://openalex.org/W2586550226","https://openalex.org/W2747023022","https://openalex.org/W2898609816","https://openalex.org/W2930078620","https://openalex.org/W2963388230","https://openalex.org/W3008036376","https://openalex.org/W3093068657","https://openalex.org/W3105711480","https://openalex.org/W3165735742","https://openalex.org/W4242273588","https://openalex.org/W4296951292","https://openalex.org/W4301866048"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W4386937951","https://openalex.org/W2042875514","https://openalex.org/W2999616507","https://openalex.org/W3098963165","https://openalex.org/W4392238179","https://openalex.org/W3164276969","https://openalex.org/W2029287765","https://openalex.org/W2043671984"],"abstract_inverted_index":{"Abstract":[0],"We":[1,159],"consider":[2],"systems":[3],"of":[4,23,49,56,74,118,142,163,174],"ordinary":[5],"differential":[6],"equations":[7],"with":[8,85],"multiple":[9],"scales":[10,91],"in":[11,18,59,121],"time.":[12],"In":[13],"general,":[14],"we":[15,62,109,123],"are":[16,44,54,92],"interested":[17],"the":[19,40,47,50,72,75,132,143,150,156,161,164],"long":[20],"time":[21],"horizon":[22],"a":[24,36,65,115,126,140,175],"slow":[25,90,151],"variable":[26],"that":[27,33,69,80,137],"is":[28],"coupled":[29,51],"to":[30,114],"solution":[31],"components":[32],"act":[34],"on":[35,131,149,155],"fast":[37,41,101,157],"scale.":[38,158],"Although":[39],"scale":[42,102,152],"variables":[43],"essential":[45],"for":[46,82,139,171],"dynamics":[48],"problem,":[52],"they":[53],"often":[55],"no":[57],"interest":[58],"themselves.":[60],"Recently,":[61],"have":[63],"proposed":[64],"temporal":[66],"multiscale":[67,77,112,177],"approach":[68,113],"fits":[70],"into":[71,145],"framework":[73],"heterogeneous":[76],"method":[78,136],"and":[79,89,98,153,167],"allows":[81,138],"efficient":[83],"simulations":[84],"significant":[86],"speedups.":[87],"Fast":[88],"decoupled":[93],"by":[94,99,104],"introducing":[95],"local":[96],"averages":[97],"replacing":[100],"contributions":[103],"localized":[105],"periodic-in-time":[106],"problems.":[107],"Here,":[108],"generalize":[110],"this":[111],"larger":[116],"class":[117],"problems,":[119],"but":[120],"particular,":[122],"derive":[124],"an":[125],"posteriori":[127],"error":[128,144,148,154,165],"estimator":[129,166],"based":[130],"dual":[133],"weighted":[134],"residual":[135],"splitting":[141],"averaging":[146],"error,":[147],"demonstrate":[160],"accuracy":[162],"also":[168],"its":[169],"use":[170],"adaptive":[172],"control":[173],"numerical":[176],"scheme.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
