{"id":"https://openalex.org/W7214039739","doi":"https://doi.org/10.48550/arxiv.2609.24268","title":"A subcell-refined entropy-residual-driven limiting strategy for high-order discontinuous Galerkin methods","display_name":"A subcell-refined entropy-residual-driven limiting strategy for high-order discontinuous Galerkin methods","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214039739","doi":"https://doi.org/10.48550/arxiv.2609.24268"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24268","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24268","pdf_url":"https://arxiv.org/pdf/2609.24268","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.24268","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101958865","display_name":"Liang Geng","orcid":"https://orcid.org/0000-0003-4697-7143","observed_orcids":["https://orcid.org/0000-0003-4697-7143"]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang, Geng","raw_affiliation_strings":["School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152450382","display_name":"Rui Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Rui","raw_affiliation_strings":["School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152474158","display_name":"Junjie Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Junjie","raw_affiliation_strings":["School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152492022","display_name":"Feng Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Feng","raw_affiliation_strings":["School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152486037","display_name":"Xinlong Feng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng, Xinlong","raw_affiliation_strings":["School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100519601","display_name":"Hui Xu","orcid":"https://orcid.org/0000-0001-8448-4425","observed_orcids":["https://orcid.org/0000-0001-8448-4425","https://orcid.org/0000-0002-4758-2031"]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]},{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Hui","raw_affiliation_strings":["College of Mathematics and System Sciences , Xinjiang University , Urumqi 830046 , P.R. China","School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Sciences , Xinjiang University , Urumqi 830046 , P.R. China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"School of Aeronautics and Astronautics , Shanghai Jiao Tong University , Shanghai , 200240 , China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9940999746322632,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9940999746322632,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.00570000009611249,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/high-order-discontinuous-galerkin-method","display_name":"high-order discontinuous Galerkin method","score":0.8759999871253967},{"id":"https://openalex.org/keywords/entropy-stable-schemes","display_name":"entropy stable schemes","score":0.7020000219345093},{"id":"https://openalex.org/keywords/nonlinear-hyperbolic-systems","display_name":"nonlinear hyperbolic systems","score":0.8169999718666077},{"id":"https://openalex.org/keywords/under-resolved-simulation","display_name":"under-resolved simulation","score":0.8669999837875366},{"id":"https://openalex.org/keywords/positivity-preservation","display_name":"positivity preservation","score":0.6980000138282776},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.7350000143051147},{"id":"https://openalex.org/keywords/entropy-generation","display_name":"entropy production","score":0.753000020980835},{"id":"https://openalex.org/keywords/jump-operator","display_name":"jump operator","score":0.5690000057220459},{"id":"https://openalex.org/keywords/entropy-inequality","display_name":"entropy inequality","score":0.5059999823570251}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7883999943733215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7127000093460083},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.685699999332428},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C45011657","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiter","level":2,"score":0.5238000154495239},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5092999935150146},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5016000270843506},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46470001339912415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38760000467300415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3824999928474426},{"id":"https://openalex.org/C207282930","wikidata":"https://www.wikidata.org/wiki/Q5380811","display_name":"Entropy production","level":2,"score":0.3549000024795532},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32429999113082886},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.2976999878883362},{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.2727000117301941},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24268","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24268","pdf_url":"https://arxiv.org/pdf/2609.24268","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.24268","doi":"https://doi.org/10.48550/arxiv.2609.24268","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24268","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.24268","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24268","pdf_url":"https://arxiv.org/pdf/2609.24268","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214039739.pdf","grobid_xml":"https://content.openalex.org/works/W7214039739.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4414757729"],"related_works":["https://openalex.org/W7163653294","https://openalex.org/W4389298379","https://openalex.org/W7147213933","https://openalex.org/W4290830034","https://openalex.org/W7223375229","https://openalex.org/W3100603004","https://openalex.org/W2900397291","https://openalex.org/W7203526264","https://openalex.org/W2028525550","https://openalex.org/W7131875023"],"abstract_inverted_index":{"Fine-grained,":[0],"subcell-level":[1],"dissipation":[2,43,54],"control":[3],"is":[4,64],"essential":[5],"for":[6,32],"achieving":[7],"robust":[8],"high-order":[9,136],"discontinuous":[10],"Galerkin":[11],"(DG)":[12],"simulations":[13],"of":[14,70,90,119,147],"nonlinear":[15],"hyperbolic":[16],"systems":[17],"in":[18],"under-resolved":[19],"regimes":[20],"while":[21,110],"preserving":[22,111],"accuracy.":[23],"This":[24],"paper":[25],"proposes":[26],"a":[27,65,75,98,116,148],"subcell-refined":[28],"entropy-residual-driven":[29],"limiting":[30,92],"strategy":[31,63],"DG":[33,81],"on":[34],"Legendre-Gauss-Lobatto":[35],"nodes.":[36],"The":[37,62],"limiter":[38,123],"introduces":[39],"only":[40],"nearest-neighbor":[41],"pairwise":[42],"within":[44],"each":[45],"element,":[46],"with":[47],"closed-form":[48],"coefficients":[49],"that":[50,131],"supply":[51],"the":[52,58,91,95,120,132,145],"minimal":[53],"required":[55],"to":[56],"restore":[57],"element":[59],"entropy":[60,84,108,140],"inequality.":[61],"diagonal,":[66],"locally":[67],"stable":[68],"approximation":[69],"classical":[71],"entropy-stable":[72],"methods,":[73],"and":[74,82,106,113,142],"generalized":[76],"subcell":[77,117],"framework":[78],"reveals":[79],"split-form":[80],"residual-distribution-based":[83],"correction":[85],"schemes":[86],"as":[87],"particular":[88],"choices":[89],"coefficients.":[93],"For":[94],"Euler":[96],"equations,":[97],"physically":[99],"consistent":[100],"jump":[101],"operator":[102],"separately":[103],"models":[104],"thermal":[105],"shear":[107],"production":[109],"velocity":[112],"pressure":[114],"equilibrium;":[115],"refinement":[118],"Zhang-Shu":[121],"positivity":[122],"ensures":[124],"pointwise":[125],"positivity.":[126],"Extensive":[127],"numerical":[128],"tests":[129],"confirm":[130],"scheme":[133],"maintains":[134],"optimal":[135],"accuracy,":[137],"strictly":[138],"enforces":[139],"dissipation,":[141],"significantly":[143],"reduces":[144],"difficulty":[146],"posteriori":[149],"positivity-preserving":[150],"procedures.":[151]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
