{"id":"https://openalex.org/W4389886089","doi":"https://doi.org/10.1007/s00211-023-01386-4","title":"A super-localized generalized finite element method","display_name":"A super-localized generalized finite element method","publication_year":2023,"publication_date":"2023-12-18","ids":{"openalex":"https://openalex.org/W4389886089","doi":"https://doi.org/10.1007/s00211-023-01386-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01386-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01386-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01386-4.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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01386-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076713066","display_name":"Philip Freese","orcid":"https://orcid.org/0000-0002-9838-6321"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philip Freese","raw_affiliation_strings":["Institute of Mathematics, Hamburg University of Technology, Am Schwarzenberg-Campus 3, 21073, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hamburg University of Technology, Am Schwarzenberg-Campus 3, 21073, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017279001","display_name":"Moritz Hauck","orcid":"https://orcid.org/0000-0003-4817-9727"},"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":true,"raw_author_name":"Moritz Hauck","raw_affiliation_strings":["Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology, 41296, G\u00f6teborg, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Gothenburg and Chalmers University of Technology, 41296, G\u00f6teborg, Sweden","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065568767","display_name":"Tim Keil","orcid":null},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tim Keil","raw_affiliation_strings":["Institute of Analysis and Numerics and Mathematics M\u00fcnster, University of M\u00fcnster, Einsteinstr. 62, 48149, M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Numerics and Mathematics M\u00fcnster, University of M\u00fcnster, Einsteinstr. 62, 48149, M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014228488","display_name":"Daniel Peterseim","orcid":"https://orcid.org/0000-0001-7213-556X"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Peterseim","raw_affiliation_strings":["Institute of Mathematics and Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universit\u00e4tsstr. 12a, 86159, Augsburg, Germany","Institute of Mathematics and Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universit\u00e4tsstr.\u00a012a, 86159, Augsburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universit\u00e4tsstr. 12a, 86159, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Institute of Mathematics and Centre for Advanced Analytics and Predictive Sciences (CAAPS), University of Augsburg, Universit\u00e4tsstr.\u00a012a, 86159, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5017279001"],"corresponding_institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.8429,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.8786193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"156","issue":"1","first_page":"205","last_page":"235"},"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":0.9998999834060669,"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":0.9994000196456909,"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/mathematics","display_name":"Mathematics","score":0.8260565400123596},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7305675745010376},{"id":"https://openalex.org/keywords/partition-of-unity","display_name":"Partition of unity","score":0.6445572376251221},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.6233945488929749},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5672659873962402},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.555126965045929},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.535467803478241},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.510424792766571},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4796193540096283},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.46063244342803955},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42177626490592957},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4111612141132355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35951608419418335},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2993197441101074}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8260565400123596},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7305675745010376},{"id":"https://openalex.org/C102205669","wikidata":"https://www.wikidata.org/wiki/Q191690","display_name":"Partition of unity","level":3,"score":0.6445572376251221},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.6233945488929749},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5672659873962402},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.555126965045929},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.535467803478241},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.510424792766571},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4796193540096283},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.46063244342803955},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42177626490592957},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4111612141132355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35951608419418335},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2993197441101074},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-023-01386-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01386-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01386-4.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:research.chalmers.se:539042","is_oa":true,"landing_page_url":"https://research.chalmers.se/en/publication/539042","pdf_url":"https://research.chalmers.se/publication/539042/file/539042_Fulltext.pdf","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":null},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:107307","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/107307","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/107307/107307.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"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":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01386-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01386-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01386-4.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":[{"id":"https://openalex.org/G1652504919","display_name":null,"funder_award_id":"EXC 2044","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2817606592","display_name":"EXC 2044: Mathematik M\u00fcnster: Dynamik \u2013 Geometrie \u2013 Struktur","funder_award_id":"390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6938060324","display_name":null,"funder_award_id":"EXC2044390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323421","display_name":"G\u00f6teborgs Universitet","ror":"https://ror.org/01tm6cn81"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389886089.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1980404981","https://openalex.org/W1983122553","https://openalex.org/W1983731750","https://openalex.org/W2034705487","https://openalex.org/W2060368109","https://openalex.org/W2061480843","https://openalex.org/W2082741499","https://openalex.org/W2092011174","https://openalex.org/W2126028850","https://openalex.org/W2513676926","https://openalex.org/W2724669522","https://openalex.org/W2956858360","https://openalex.org/W2963634130","https://openalex.org/W2979712029","https://openalex.org/W3100409126","https://openalex.org/W3103355665","https://openalex.org/W3109896535","https://openalex.org/W3136924005","https://openalex.org/W3152831002","https://openalex.org/W3184443968","https://openalex.org/W3198272795","https://openalex.org/W3211939599","https://openalex.org/W4210324329","https://openalex.org/W4226345115","https://openalex.org/W4248482327","https://openalex.org/W4281701542","https://openalex.org/W4298356938","https://openalex.org/W4299521717","https://openalex.org/W4306706756","https://openalex.org/W4308241234","https://openalex.org/W4310426000","https://openalex.org/W4385187474","https://openalex.org/W6931408412"],"related_works":["https://openalex.org/W2089909466","https://openalex.org/W3208000705","https://openalex.org/W2089799198","https://openalex.org/W2126034343","https://openalex.org/W3193597985","https://openalex.org/W2104620528","https://openalex.org/W1984215587","https://openalex.org/W2381320429","https://openalex.org/W2593957634","https://openalex.org/W2352690124"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"presents":[3],"a":[4,61,85,87,90,100],"novel":[5],"multi-scale":[6],"method":[7,24],"for":[8,112],"elliptic":[9],"partial":[10],"differential":[11],"equations":[12],"with":[13,29,37],"arbitrarily":[14],"rough":[15],"coefficients.":[16,116],"In":[17,105],"the":[18,23,38,44,109],"spirit":[19],"of":[20,63,102],"numerical":[21,103],"homogenization,":[22],"constructs":[25],"problem-adapted":[26],"ansatz":[27],"spaces":[28],"uniform":[30],"algebraic":[31],"approximation":[32,77],"rates.":[33],"Localized":[34],"basis":[35,56],"functions":[36],"same":[39],"super-exponential":[40],"localization":[41,81],"properties":[42],"as":[43],"recently":[45],"proposed":[46],"Super-Localized":[47],"Orthogonal":[48],"Decomposition":[49],"enable":[50],"an":[51],"efficient":[52],"implementation.":[53],"The":[54],"method\u2019s":[55,110],"stability":[57],"is":[58,72],"enforced":[59],"using":[60],"partition":[62],"unity":[64],"approach.":[65],"A":[66],"natural":[67],"extension":[68],"to":[69],"higher":[70,76],"order":[71],"presented,":[73],"resulting":[74],"in":[75,99],"rates":[78],"and":[79,89,94],"enhanced":[80],"properties.":[82],"We":[83],"perform":[84],"rigorous":[86],"priori":[88],"posteriori":[91],"error":[92],"analysis":[93],"confirm":[95],"our":[96],"theoretical":[97],"findings":[98],"series":[101],"experiments.":[104],"particular,":[106],"we":[107],"demonstrate":[108],"applicability":[111],"challenging":[113],"high-contrast":[114],"channeled":[115]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
