{"id":"https://openalex.org/W4411628857","doi":"https://doi.org/10.1515/jnma-2024-0123","title":"Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems","display_name":"Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems","publication_year":2025,"publication_date":"2025-06-25","ids":{"openalex":"https://openalex.org/W4411628857","doi":"https://doi.org/10.1515/jnma-2024-0123"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2024-0123","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0123","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1515/jnma-2024-0123","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090390734","display_name":"Dmitri Kuzmin","orcid":"https://orcid.org/0000-0003-0084-9752"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dmitri Kuzmin","raw_affiliation_strings":["Institute of Applied Mathematics (LS III) , TU Dortmund University , Dortmund , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics (LS III) , TU Dortmund University , Dortmund , Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077357327","display_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvi\u010fov\u00e1","orcid":"https://orcid.org/0000-0002-4351-0161"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M\u00e1ria Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1","raw_affiliation_strings":["Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006640870","display_name":"Philipp \u00d6ffner","orcid":"https://orcid.org/0000-0002-1367-1917"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]},{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philipp \u00d6ffner","raw_affiliation_strings":["Institute of Mathematics , Clausthal University of Technology , Clausthal-Zellerfeld , Germany","Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany"],"raw_orcid":"https://orcid.org/0000-0002-1367-1917","affiliations":[{"raw_affiliation_string":"Institute of Mathematics , Clausthal University of Technology , Clausthal-Zellerfeld , Germany","institution_ids":["https://openalex.org/I43980791"]},{"raw_affiliation_string":"Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2400,"currency":"EUR","value_usd":2712},"apc_paid":{"value":2400,"currency":"EUR","value_usd":2712},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10592535,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"1","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8462398052215576},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6992073059082031},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6491154432296753},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6309609413146973},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6116796731948853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5074133276939392},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4949316382408142},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4162883758544922},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21097880601882935},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.056149572134017944}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8462398052215576},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6992073059082031},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6491154432296753},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6309609413146973},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6116796731948853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5074133276939392},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4949316382408142},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4162883758544922},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21097880601882935},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.056149572134017944},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2024-0123","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0123","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/jnma-2024-0123","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0123","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W617954470","https://openalex.org/W1491026465","https://openalex.org/W1678037008","https://openalex.org/W1980520313","https://openalex.org/W1990596161","https://openalex.org/W2043057066","https://openalex.org/W2064969572","https://openalex.org/W2072226973","https://openalex.org/W2105885712","https://openalex.org/W2129822331","https://openalex.org/W2229134066","https://openalex.org/W2400738778","https://openalex.org/W2787285842","https://openalex.org/W2806223757","https://openalex.org/W2962976992","https://openalex.org/W2964325435","https://openalex.org/W2964821384","https://openalex.org/W2982174245","https://openalex.org/W2982331527","https://openalex.org/W3010658891","https://openalex.org/W3013974629","https://openalex.org/W3089704316","https://openalex.org/W3099787986","https://openalex.org/W3102254702","https://openalex.org/W3158305113","https://openalex.org/W3165947770","https://openalex.org/W3183178141","https://openalex.org/W3208447861","https://openalex.org/W4205791012","https://openalex.org/W4237110413","https://openalex.org/W4253766729","https://openalex.org/W4292081050","https://openalex.org/W4294591104","https://openalex.org/W4297820717","https://openalex.org/W4313549260","https://openalex.org/W4366131625"],"related_works":["https://openalex.org/W2021654023","https://openalex.org/W4254088695","https://openalex.org/W2367880982","https://openalex.org/W2477411237","https://openalex.org/W1964128728","https://openalex.org/W2360811052","https://openalex.org/W2112506890","https://openalex.org/W2077845843","https://openalex.org/W206336013","https://openalex.org/W2502579552"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"investigate":[2],"the":[3,13,36,47,59,65,70,78,82,93,104,113,126,134],"consistency":[4],"and":[5,30,112],"convergence":[6,80],"of":[7,15,43,49,64,73,81,128],"flux-corrected":[8,83],"finite":[9,84],"element":[10,85],"approximations":[11,130],"in":[12,99],"context":[14],"nonlinear":[16],"hyperbolic":[17],"conservation":[18],"laws.":[19],"In":[20],"particular,":[21],"we":[22,76],"focus":[23],"on":[24,53],"a":[25,32,50,88,96,122],"monolithic":[26],"convex":[27],"limiting":[28],"approach":[29],"prove":[31,77],"Lax\u2013Wendroff-type":[33],"theorem":[34],"for":[35],"corresponding":[37],"semi-discrete":[38,60],"problem.":[39],"A":[40],"key":[41],"component":[42],"our":[44],"analysis":[45],"is":[46,106,115],"use":[48],"weak":[51,79,90],"estimate":[52],"bounded":[54,108,117],"variation,":[55],"which":[56],"follows":[57],"from":[58,110,118],"entropy":[61],"stability":[62],"property":[63],"method":[66],"under":[67,92],"investigation.":[68],"For":[69],"Euler":[71],"equations":[72],"gas":[74,97],"dynamics,":[75],"scheme":[86],"to":[87,133],"dissipative":[89],"solution":[91,124],"assumption":[94],"that":[95],"stays":[98],"physically":[100],"reasonable":[101],"region,":[102],"i.e.,":[103],"density":[105],"uniformly":[107,116],"away":[109],"zero,":[111],"energy":[114],"above.":[119],"Furthermore,":[120],"if":[121],"strong":[123,135],"exists,":[125],"sequence":[127],"numerical":[129],"converges":[131],"strongly":[132],"solution.":[136]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}