{"id":"https://openalex.org/W4297820717","doi":"https://doi.org/10.1137/21m1431011","title":"On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field","display_name":"On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4297820717","doi":"https://doi.org/10.1137/21m1431011"},"language":"en","primary_location":{"id":"doi:10.1137/21m1431011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1431011","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/A5100421450","display_name":"Yang Li","orcid":"https://orcid.org/0000-0002-2004-1198"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060096853","display_name":"Bangwei She","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bangwei She","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5025-0070","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100421450"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1347,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.87197881,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"60","issue":"4","first_page":"2182","last_page":"2202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976999759674072,"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":0.996399998664856,"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/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.7734524011611938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7160272598266602},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6652238965034485},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6584370136260986},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.6340665817260742},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.5510193109512329},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4617047905921936},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4108654856681824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21499353647232056},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.19917592406272888}],"concepts":[{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.7734524011611938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7160272598266602},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6652238965034485},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6584370136260986},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.6340665817260742},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.5510193109512329},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4617047905921936},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4108654856681824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21499353647232056},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.19917592406272888},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1431011","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1431011","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4384265194","display_name":null,"funder_award_id":"12001003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5846434524","display_name":null,"funder_award_id":"21-02411S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W592911714","https://openalex.org/W2020392194","https://openalex.org/W2082029579","https://openalex.org/W2110634732","https://openalex.org/W2147277530","https://openalex.org/W2166287567","https://openalex.org/W2205510167","https://openalex.org/W2325379949","https://openalex.org/W2331053393","https://openalex.org/W2748749923","https://openalex.org/W2791888879","https://openalex.org/W2980506174","https://openalex.org/W2999018210","https://openalex.org/W3092976532","https://openalex.org/W4205791012","https://openalex.org/W4287271306"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2165272709","https://openalex.org/W1999937375","https://openalex.org/W1971908644","https://openalex.org/W2375053028","https://openalex.org/W1981749300","https://openalex.org/W2373502461","https://openalex.org/W586558997","https://openalex.org/W3123775475","https://openalex.org/W2295113609"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,18,54,60,108],"general":[3],"convergence":[4,77,113,154],"theory":[5],"for":[6],"the":[7,25,35,48,69,76,82,88,93,97,121,156,161],"numerical":[8,21,103],"solutions":[9,41,104,143],"of":[10,28,38,78,101,123,144],"compressible":[11],"viscous":[12],"and":[13,42,86,99,116,160],"electrically":[14],"conducting":[15],"fluids":[16],"with":[17,59,134],"focus":[19],"on":[20],"schemes":[22,147],"that":[23,142],"preserve":[24],"divergence-free":[26,136],"property":[27],"magnetic":[29,137],"field":[30],"exactly.":[31],"Our":[32],"strategy":[33],"utilizes":[34],"recent":[36],"concepts":[37],"dissipative":[39,49,55,83,157],"weak":[40,56,84,158],"consistent":[43,79,94,149],"approximations.":[44],"First,":[45],"we":[46,74,105,126,151],"show":[47,75],"weak--strong":[50],"uniqueness":[51],"principle,":[52],"meaning":[53],"solution":[57,62,85,159],"coincides":[58],"classical":[61,89,162],"as":[63,65,96],"long":[64],"they":[66],"emanate":[67],"from":[68],"same":[70],"initial":[71],"data.":[72],"Next,":[73],"approximation":[80,95],"toward":[81,155],"thus":[87],"solution.":[90,163],"Upon":[91],"interpreting":[92],"stability":[98,115],"consistency":[100],"suitable":[102],"have":[106],"established":[107],"generalized":[109],"Lax":[110],"equivalence":[111],"theory:":[112],"$\\Longleftrightarrow$":[114],"consistency.":[117],"Further,":[118],"to":[119],"illustrate":[120],"application":[122],"this":[124],"theory,":[125],"propose":[127],"two":[128,146],"mixed":[129],"finite":[130],"volume--finite":[131],"element":[132],"methods":[133],"exact":[135],"field.":[138],"Finally,":[139],"by":[140],"showing":[141],"these":[145],"are":[148],"approximations,":[150],"conclude":[152],"their":[153]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}