{"id":"https://openalex.org/W2716150740","doi":"https://doi.org/10.1137/17m1147044","title":"Residual-Based Variational Multiscale Modeling in a Discontinuous Galerkin Framework","display_name":"Residual-Based Variational Multiscale Modeling in a Discontinuous Galerkin Framework","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2716150740","doi":"https://doi.org/10.1137/17m1147044","mag":"2716150740"},"language":"en","primary_location":{"id":"doi:10.1137/17m1147044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1147044","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 &amp; Simulation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1709.03934","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003011794","display_name":"Stein K.F. Stoter","orcid":"https://orcid.org/0000-0001-5845-4900"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stein K.F. Stoter","raw_affiliation_strings":["University of Minnesota\u2010Twin Cities"],"raw_orcid":"https://orcid.org/0000-0001-5845-4900","affiliations":[{"raw_affiliation_string":"University of Minnesota\u2010Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088827344","display_name":"Sergio Turteltaub","orcid":"https://orcid.org/0000-0003-3706-9100"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sergio R. Turteltaub","raw_affiliation_strings":["(Delft University of Technology)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Delft University of Technology)","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006667269","display_name":"Steven J. Hulshoff","orcid":"https://orcid.org/0000-0002-3669-0977"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Steven J. Hulshoff","raw_affiliation_strings":["(Delft University of Technology)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"(Delft University of Technology)","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040889195","display_name":"Dominik Schillinger","orcid":"https://orcid.org/0000-0002-9068-6311"},"institutions":[{"id":"https://openalex.org/I4210162610","display_name":"Grantmakers for Effective Organizations","ror":"https://ror.org/0501kzx55","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210162610"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dominik Schillinger","raw_affiliation_strings":["Civil, Environmental, and Geo- Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Civil, Environmental, and Geo- Engineering","institution_ids":["https://openalex.org/I4210162610"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003011794"],"corresponding_institution_ids":["https://openalex.org/I130238516","https://openalex.org/I4210101327"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02260394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"3","first_page":"1333","last_page":"1364"},"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/T11558","display_name":"Composite Material Mechanics","score":0.9954000115394592,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8634889125823975},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.6660985350608826},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5727944374084473},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5649343132972717},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5520879030227661},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.513372540473938},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.48878785967826843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4467388987541199},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.4438934922218323},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.42672842741012573},{"id":"https://openalex.org/keywords/scale-model","display_name":"Scale model","score":0.4115440845489502},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4067001938819885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3845599889755249},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34726274013519287},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20709946751594543},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19220447540283203},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16900423169136047}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8634889125823975},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.6660985350608826},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5727944374084473},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5649343132972717},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5520879030227661},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.513372540473938},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.48878785967826843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4467388987541199},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.4438934922218323},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.42672842741012573},{"id":"https://openalex.org/C152588345","wikidata":"https://www.wikidata.org/wiki/Q6498959","display_name":"Scale model","level":2,"score":0.4115440845489502},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4067001938819885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3845599889755249},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34726274013519287},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20709946751594543},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19220447540283203},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16900423169136047},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/17m1147044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1147044","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 &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:154983","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Stoter=3AStein_K=2EF=2E=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:arXiv.org:1709.03934","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03934","pdf_url":"https://arxiv.org/pdf/1709.03934","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":null,"raw_type":"text"},{"id":"pmh:oai:tudelft.nl:uuid:29e7c33d-5c07-4341-868f-b5f2c1c40302","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:29e7c33d-5c07-4341-868f-b5f2c1c40302","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"master thesis"},{"id":"pmh:oai:tudelft.nl:uuid:b4fccf77-cd61-4434-9959-67670a39df38","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:b4fccf77-cd61-4434-9959-67670a39df38","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},{"id":"doi:10.48550/arxiv.1709.03934","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.03934","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"},{"id":"mag:2716150740","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1709.03934","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03934","pdf_url":"https://arxiv.org/pdf/1709.03934","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3284611676","display_name":null,"funder_award_id":"1651577","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W49087508","https://openalex.org/W49566120","https://openalex.org/W98676337","https://openalex.org/W222841820","https://openalex.org/W1560684774","https://openalex.org/W1585098889","https://openalex.org/W1628714285","https://openalex.org/W1788335260","https://openalex.org/W1908859542","https://openalex.org/W1974535188","https://openalex.org/W1976136035","https://openalex.org/W1979560958","https://openalex.org/W1996858170","https://openalex.org/W1998894128","https://openalex.org/W2004494416","https://openalex.org/W2009204009","https://openalex.org/W2012938047","https://openalex.org/W2018060978","https://openalex.org/W2019518140","https://openalex.org/W2029017626","https://openalex.org/W2030066057","https://openalex.org/W2051736601","https://openalex.org/W2070033465","https://openalex.org/W2073897969","https://openalex.org/W2074769980","https://openalex.org/W2078045751","https://openalex.org/W2079263908","https://openalex.org/W2079816657","https://openalex.org/W2085304822","https://openalex.org/W2092649395","https://openalex.org/W2100903519","https://openalex.org/W2125187234","https://openalex.org/W2125494828","https://openalex.org/W2130350269","https://openalex.org/W2149374694","https://openalex.org/W2154122281","https://openalex.org/W2162005195","https://openalex.org/W2165123564","https://openalex.org/W2206365535","https://openalex.org/W2471856754","https://openalex.org/W2963785805","https://openalex.org/W3005021337"],"related_works":["https://openalex.org/W2775151460","https://openalex.org/W600694708","https://openalex.org/W3021508334","https://openalex.org/W2174886685","https://openalex.org/W3082375637","https://openalex.org/W3047755746","https://openalex.org/W2951349796","https://openalex.org/W2110901016","https://openalex.org/W2071515778","https://openalex.org/W2591607401","https://openalex.org/W1526698283","https://openalex.org/W2007512666","https://openalex.org/W2669938236","https://openalex.org/W2911571122","https://openalex.org/W2566316804","https://openalex.org/W1992223056","https://openalex.org/W2527411328","https://openalex.org/W1985289860","https://openalex.org/W3082251716","https://openalex.org/W1555642721"],"abstract_inverted_index":{"We":[0,94],"develop":[1],"the":[2,6,20,23,97,108,126,144],"general":[3],"form":[4],"of":[5,22,41,58,76,88],"variational":[7],"multiscale":[8,122],"method":[9,16],"in":[10,56,86],"a":[11,49,59,89,129],"discontinuous":[12,27,30,103,133],"Galerkin":[13,104,134],"framework.":[14],"Our":[15],"is":[17,141],"based":[18],"on":[19,132],"decomposition":[21],"true":[24],"solution":[25],"into":[26,65],"coarse-scale":[28,35],"and":[29,136],"fine-scale":[31,42,50,67,78,91,118,166],"parts.":[32],"The":[33,44,72,121],"obtained":[34],"weak":[36],"formulation":[37,123],"includes":[38],"two":[39],"types":[40],"contributions.":[43],"first":[45],"type":[46,74],"corresponds":[47],"to":[48],"volumetric":[51,165],"term,":[52],"which":[53,83],"we":[54,84,149],"formulate":[55,85],"terms":[57,79,87],"residual-based":[60],"model":[61],"that":[62,101,151],"also":[63],"takes":[64],"account":[66],"effects":[68],"at":[69,80],"element":[70,81],"interfaces.":[71],"second":[73],"consists":[75],"independent":[77],"interfaces,":[82],"new":[90,130],"\u201cinterface":[92],"model.\u201d":[93],"demonstrate":[95],"for":[96,128,143,163],"one-dimensional":[98,145],"Poisson":[99],"problem":[100],"existing":[102],"formulations,":[105],"such":[106],"as":[107,158],"interior":[109],"penalty":[110],"method,":[111],"can":[112,155],"be":[113,156],"rederived":[114],"by":[115],"choosing":[116],"particular":[117],"interface":[119],"models.":[120],"thus":[124],"opens":[125],"door":[127],"perspective":[131],"methods":[135],"their":[137],"numerical":[138,153],"properties.":[139],"This":[140],"demonstrated":[142],"advection-diffusion":[146],"problem,":[147],"where":[148],"show":[150],"upwind":[152],"fluxes":[154],"interpreted":[157],"an":[159],"ad":[160],"hoc":[161],"remedy":[162],"missing":[164],"terms.":[167]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
