{"id":"https://openalex.org/W2099947844","doi":"https://doi.org/10.1137/120863162","title":"An Adaptive Discontinuous Galerkin Multiscale Method for Elliptic Problems","display_name":"An Adaptive Discontinuous Galerkin Multiscale Method for Elliptic Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2099947844","doi":"https://doi.org/10.1137/120863162","mag":"2099947844"},"language":"en","primary_location":{"id":"doi:10.1137/120863162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120863162","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 & 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/A5045390493","display_name":"Daniel Elfverson","orcid":"https://orcid.org/0000-0002-1710-8494"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Elfverson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103928074","display_name":"Emmanuil H. Georgoulis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanuil H. Georgoulis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062737668","display_name":"Axel M\u00e5lqvist","orcid":"https://orcid.org/0000-0002-1885-8019"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Axel M\u00e5lqvist","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3522,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92393198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"3","first_page":"747","last_page":"765"},"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/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.7996381521224976},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7220684885978699},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.717994213104248},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6024401187896729},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5430237054824829},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.5146290063858032},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4950851500034332},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49495595693588257},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.47984573245048523},{"id":"https://openalex.org/keywords/adaptive-algorithm","display_name":"Adaptive algorithm","score":0.4658110439777374},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.45865297317504883},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4551435112953186},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4503641128540039},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.44167301058769226},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4317992031574249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42160531878471375},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41948121786117554},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3567107617855072},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2243560552597046},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.1592005491256714}],"concepts":[{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.7996381521224976},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7220684885978699},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.717994213104248},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6024401187896729},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5430237054824829},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.5146290063858032},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4950851500034332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49495595693588257},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.47984573245048523},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.4658110439777374},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.45865297317504883},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4551435112953186},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4503641128540039},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.44167301058769226},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4317992031574249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42160531878471375},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41948121786117554},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3567107617855072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2243560552597046},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.1592005491256714},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120863162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120863162","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 & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W46814297","https://openalex.org/W49087508","https://openalex.org/W140909251","https://openalex.org/W202835528","https://openalex.org/W251033174","https://openalex.org/W359661129","https://openalex.org/W377201621","https://openalex.org/W628726389","https://openalex.org/W965907625","https://openalex.org/W1583515859","https://openalex.org/W1600997507","https://openalex.org/W1976683619","https://openalex.org/W1980404981","https://openalex.org/W1991960225","https://openalex.org/W1997703844","https://openalex.org/W2001660127","https://openalex.org/W2003438645","https://openalex.org/W2008987050","https://openalex.org/W2014983931","https://openalex.org/W2017073125","https://openalex.org/W2029725158","https://openalex.org/W2029918260","https://openalex.org/W2033606210","https://openalex.org/W2053162126","https://openalex.org/W2063200750","https://openalex.org/W2065713338","https://openalex.org/W2070006753","https://openalex.org/W2070033465","https://openalex.org/W2078045751","https://openalex.org/W2086501907","https://openalex.org/W2092614367","https://openalex.org/W2130350269","https://openalex.org/W2145615852","https://openalex.org/W2157721313","https://openalex.org/W4245820193","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4285069850","https://openalex.org/W2891970004","https://openalex.org/W2120874885","https://openalex.org/W2030318355","https://openalex.org/W2162026849","https://openalex.org/W2298673793","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2811078165","https://openalex.org/W1988388557"],"abstract_inverted_index":{"An":[0],"adaptive":[1,76,134],"discontinuous":[2],"Galerkin":[3],"multiscale":[4],"method":[5,18],"driven":[6],"by":[7],"an":[8,75],"energy":[9],"norm":[10],"a":[11,26,48,68,144],"posteriori":[12,69],"error":[13,70],"bound":[14,71],"is":[15,19,72,116],"proposed.":[16],"The":[17,53,67,103,125],"based":[20],"on":[21,38,94],"splitting":[22],"the":[23,41,64,80,84,88,91,96,120,128,130,133,137],"problem":[24],"into":[25],"coarse":[27,50,54],"and":[28,43,87,136],"fine":[29,32,97,104,122],"scale.":[30],"Localized":[31],"scale":[33,51,55,98,105,123],"constituent":[34,99,121],"problems":[35,100],"are":[36,44,101,107,141],"solved":[37],"patches":[39,93],"of":[40,61,90,127,132,146],"domain":[42],"used":[45,73],"to":[46,78],"obtain":[47],"modified":[49],"equation.":[52],"equation":[56],"has":[57],"considerably":[58],"less":[59],"degrees":[60],"freedom":[62],"than":[63],"original":[65],"problem.":[66],"within":[74],"algorithm":[77],"tune":[79],"critical":[81],"parameters,":[82],"i.e.,":[83],"refinement":[85],"level":[86],"size":[89],"different":[92,114],"which":[95],"solved.":[102],"computations":[106],"completely":[108],"parallelizable,":[109],"since":[110],"no":[111],"communication":[112],"between":[113],"processors":[115],"required":[117],"for":[118],"solving":[119],"problems.":[124],"convergence":[126],"method,":[129],"performance":[131],"strategy,":[135],"computational":[138],"effort":[139],"involved":[140],"investigated":[142],"through":[143],"series":[145],"numerical":[147],"experiments.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}