{"id":"https://openalex.org/W2246621938","doi":"https://doi.org/10.1007/s00211-017-0905-7","title":"Multiscale techniques for parabolic equations","display_name":"Multiscale techniques for parabolic equations","publication_year":2017,"publication_date":"2017-07-20","ids":{"openalex":"https://openalex.org/W2246621938","doi":"https://doi.org/10.1007/s00211-017-0905-7","mag":"2246621938"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-017-0905-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-017-0905-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-017-0905-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-017-0905-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062737668","display_name":"Axel M\u00e5lqvist","orcid":"https://orcid.org/0000-0002-1885-8019"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Axel M\u00e5lqvist","raw_affiliation_strings":["[Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, G\u00f6teborg, Sweden]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, G\u00f6teborg, Sweden]","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101902361","display_name":"A Erik G Persson","orcid":"https://orcid.org/0000-0003-3159-8239"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anna Persson","raw_affiliation_strings":["Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gteborg, Sweden 123","[Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, G\u00f6teborg, Sweden]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gteborg, Sweden 123","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"[Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, G\u00f6teborg, Sweden]","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.2393,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.52104255,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"138","issue":"1","first_page":"191","last_page":"217"},"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":0.9995999932289124,"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/T11558","display_name":"Composite Material Mechanics","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.7972050905227661},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7838234901428223},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6823606491088867},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6174901127815247},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5525524616241455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5470526814460754},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5238440036773682},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5176182985305786},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.485462486743927},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45889922976493835},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4418160021305084},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.4217476546764374},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4156593382358551},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.41456204652786255},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.22055485844612122},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14865627884864807},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11378943920135498},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.10621228814125061}],"concepts":[{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.7972050905227661},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7838234901428223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6823606491088867},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6174901127815247},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5525524616241455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5470526814460754},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5238440036773682},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5176182985305786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.485462486743927},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45889922976493835},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4418160021305084},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.4217476546764374},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4156593382358551},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.41456204652786255},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.22055485844612122},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14865627884864807},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11378943920135498},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.10621228814125061},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00211-017-0905-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-017-0905-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-017-0905-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1504.08140","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.08140","pdf_url":"https://arxiv.org/pdf/1504.08140","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1504.08140","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1504.08140","pdf_url":"https://arxiv.org/pdf/1504.08140","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},{"id":"mag:2246621938","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1504.08140.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:5762871","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5762871","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numer Math (Heidelb)","raw_type":"Text"},{"id":"pmh:oai:research.chalmers.se:500565","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/500565","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.1504.08140","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1504.08140","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00211-017-0905-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-017-0905-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00211-017-0905-7.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321523","display_name":"Chalmers Tekniska H\u00f6gskola","ror":"https://ror.org/040wg7k59"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2246621938.pdf","grobid_xml":"https://content.openalex.org/works/W2246621938.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1978691912","https://openalex.org/W1980404981","https://openalex.org/W1997703844","https://openalex.org/W2011473263","https://openalex.org/W2027748639","https://openalex.org/W2034705487","https://openalex.org/W2060368109","https://openalex.org/W2067514470","https://openalex.org/W2076074132","https://openalex.org/W2078045751","https://openalex.org/W2082621526","https://openalex.org/W2115253932","https://openalex.org/W2138940269","https://openalex.org/W2151177334","https://openalex.org/W2157935711","https://openalex.org/W2322620490","https://openalex.org/W2369386221","https://openalex.org/W2949455114","https://openalex.org/W2953193673","https://openalex.org/W3103355665"],"related_works":["https://openalex.org/W3114646235","https://openalex.org/W2963020731","https://openalex.org/W2736435178","https://openalex.org/W2971365981","https://openalex.org/W3048150682","https://openalex.org/W2971940950","https://openalex.org/W3037909252","https://openalex.org/W2535408367","https://openalex.org/W3047532276","https://openalex.org/W2985936449","https://openalex.org/W2563211547","https://openalex.org/W3135434554","https://openalex.org/W3047922823","https://openalex.org/W2946492363","https://openalex.org/W2949236226","https://openalex.org/W2766915832","https://openalex.org/W2754735025","https://openalex.org/W3099874855","https://openalex.org/W3098082781","https://openalex.org/W2308982285"],"abstract_inverted_index":{"We":[0,33,72],"use":[1],"the":[2,44,54,59,62,67],"local":[3],"orthogonal":[4],"decomposition":[5],"technique":[6],"introduced":[7],"in":[8,66],"Mlqvist":[9],"and":[10,25,38],"Peterseim":[11],"(Math":[12],"Comput":[13],"83(290):2583-2603,":[14],"2014)":[15],"to":[16],"derive":[17],"a":[18,39],"generalized":[19],"finite":[20],"element":[21],"method":[22],"for":[23,43],"linear":[24],"semilinear":[26],"parabolic":[27],"equations":[28],"with":[29],"spatial":[30],"multiscale":[31],"coefficients.":[32],"consider":[34],"nonsmooth":[35],"initial":[36],"data":[37],"backward":[40],"Euler":[41],"scheme":[42],"temporal":[45],"discretization.":[46],"Optimal":[47],"order":[48],"convergence":[49],"rate,":[50],"depending":[51],"only":[52],"on":[53,58],"contrast,":[55],"but":[56],"not":[57],"variations":[60],"of":[61],"coefficients,":[63],"is":[64],"proven":[65],"L":[68],"(L":[69],"2":[70],")-norm.":[71],"present":[73],"numerical":[74],"examples,":[75],"which":[76],"confirm":[77],"our":[78],"theoretical":[79],"findings.":[80]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}