{"id":"https://openalex.org/W2065713338","doi":"https://doi.org/10.1137/120900113","title":"Convergence of a Discontinuous Galerkin Multiscale Method","display_name":"Convergence of a Discontinuous Galerkin Multiscale Method","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2065713338","doi":"https://doi.org/10.1137/120900113","mag":"2065713338"},"language":"en","primary_location":{"id":"doi:10.1137/120900113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900113","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/A5045390493","display_name":"Daniel Elfverson","orcid":"https://orcid.org/0000-0002-1710-8494"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]},{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB","SE"],"is_corresponding":false,"raw_author_name":"Daniel Elfverson","raw_affiliation_strings":["Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden","Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden","institution_ids":["https://openalex.org/I123387679"]},{"raw_affiliation_string":"Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103928074","display_name":"Emmanuil H. Georgoulis","orcid":null},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]},{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB","SE"],"is_corresponding":false,"raw_author_name":"Emmanuil H. Georgoulis","raw_affiliation_strings":["Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK","Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK","institution_ids":["https://openalex.org/I153648349"]},{"raw_affiliation_string":"Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062737668","display_name":"Axel M\u00e5lqvist","orcid":"https://orcid.org/0000-0002-1885-8019"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]},{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB","SE"],"is_corresponding":false,"raw_author_name":"Axel M\u00e5lqvist","raw_affiliation_strings":["Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden","Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Technology, Uppsala University, Uppsala. SE-751 05, Sweden","institution_ids":["https://openalex.org/I123387679"]},{"raw_affiliation_string":"Department of Mathematics. University of Leicester, Leicester, LEI 7RH, UK","institution_ids":["https://openalex.org/I153648349"]}]},{"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/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Peterseim","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Berlin 10099, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Berlin 10099, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4492,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97624854,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"51","issue":"6","first_page":"3351","last_page":"3372"},"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":0.9998000264167786,"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":0.9987999796867371,"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":0.8147428631782532},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.7093415260314941},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.6145505309104919},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.5853428244590759},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5778648257255554},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5629044771194458},{"id":"https://openalex.org/keywords/convergence-tests","display_name":"Convergence tests","score":0.5556193590164185},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5428950190544128},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5157356858253479},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.47141051292419434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4471830427646637},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44530409574508667},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.44464507699012756},{"id":"https://openalex.org/keywords/uniform-norm","display_name":"Uniform norm","score":0.44128572940826416},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4226158857345581},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2220815122127533},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14563170075416565}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8147428631782532},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.7093415260314941},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.6145505309104919},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.5853428244590759},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5778648257255554},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5629044771194458},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.5556193590164185},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5428950190544128},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5157356858253479},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.47141051292419434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4471830427646637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44530409574508667},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.44464507699012756},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.44128572940826416},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4226158857345581},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2220815122127533},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14563170075416565},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.0},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120900113","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900113","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:uni-augsburg.opus-bayern.de:54782","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/54782","pdf_url":null,"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":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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W600694708","https://openalex.org/W1493036607","https://openalex.org/W1585098889","https://openalex.org/W1966768630","https://openalex.org/W1970588051","https://openalex.org/W1980404981","https://openalex.org/W1983122553","https://openalex.org/W1991960225","https://openalex.org/W1997703844","https://openalex.org/W2000272165","https://openalex.org/W2014983931","https://openalex.org/W2018527710","https://openalex.org/W2029725158","https://openalex.org/W2029918260","https://openalex.org/W2049248042","https://openalex.org/W2060368109","https://openalex.org/W2062771846","https://openalex.org/W2070033465","https://openalex.org/W2078045751","https://openalex.org/W2092614367","https://openalex.org/W2099947844","https://openalex.org/W2126028850","https://openalex.org/W2128778363","https://openalex.org/W2157721313","https://openalex.org/W2157935711","https://openalex.org/W2170337776","https://openalex.org/W2250850254","https://openalex.org/W2949455114","https://openalex.org/W2953346712","https://openalex.org/W2963529021","https://openalex.org/W3100150607","https://openalex.org/W4236548481"],"related_works":["https://openalex.org/W2034145661","https://openalex.org/W2028595206","https://openalex.org/W2099365622","https://openalex.org/W2482464444","https://openalex.org/W2951265198","https://openalex.org/W576291453","https://openalex.org/W2081461665","https://openalex.org/W2060809327","https://openalex.org/W4253827225","https://openalex.org/W2995787120"],"abstract_inverted_index":{"We":[0,15,101],"present":[1],"a":[2,17,43,80,88,104],"discontinuous":[3],"Galerkin":[4],"multiscale":[5,40,77],"method":[6,41],"for":[7],"second":[8],"order":[9],"elliptic":[10],"problems":[11],"and":[12,19,135],"prove":[13],"convergence.":[14,158],"consider":[16],"heterogeneous":[18],"highly":[20],"varying":[21],"diffusion":[22],"coefficient":[23],"in":[24,132,138],"$L^\\infty(\\Omega,\\mathbb{R}^{d\\times":[25],"d}_{sym})$":[26],"with":[27,62,83],"uniform":[28,81],"spectral":[29],"bounds":[30],"without":[31],"any":[32],"assumption":[33],"on":[34,49,79,122],"scale":[35],"separation":[36],"or":[37],"periodicity.":[38],"The":[39,51],"uses":[42],"corrected":[44,58,110],"basis":[45,111],"that":[46],"is":[47,92,141],"computed":[48],"patches/subdomains.":[50],"error,":[52],"due":[53],"to":[54,69,87,94,106,112],"truncation":[55],"of":[56,65,75,126,144,150,157],"the":[57,63,66,76,96,109,123,127,139,145,154],"basis,":[59],"decreases":[60],"exponentially":[61],"size":[64,85],"patches.":[67],"Hence,":[68],"achieve":[70],"an":[71],"algebraic":[72],"convergence":[73,116,131,137],"rate":[74,117],"solution":[78],"mesh":[82,84],"$H$":[86],"reference":[89],"solution,":[90],"it":[91],"sufficient":[93],"choose":[95],"patch":[97],"sizes":[98],"$\\mathcal{O}(H|\\log":[99],"H|)$.":[100],"also":[102],"discuss":[103],"way":[105],"further":[107],"localize":[108],"elementwise":[113],"support.":[114],"Improved":[115],"can":[118],"be":[119],"achieved":[120],"depending":[121],"piecewise":[124],"regularity":[125],"forcing":[128,146],"function.":[129,147],"Linear":[130],"energy":[133],"norm":[134],"quadratic":[136],"$L^2$-norm":[140],"obtained":[142],"independently":[143],"A":[148],"series":[149],"numerical":[151],"experiments":[152],"confirms":[153],"theoretical":[155],"rates":[156]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}