{"id":"https://openalex.org/W7167629950","doi":"https://doi.org/10.48550/arxiv.2607.05105","title":"Convergence analysis of a MAC scheme for the barotropic Euler system","display_name":"Convergence analysis of a MAC scheme for the barotropic Euler system","publication_year":2026,"publication_date":"2026-07-06","ids":{"openalex":"https://openalex.org/W7167629950","doi":"https://doi.org/10.48550/arxiv.2607.05105"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.05105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.05105","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.05105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060096853","display_name":"Bangwei She","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"She, Bangwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031160702","display_name":"Congying Wang","orcid":"https://orcid.org/0000-0002-7121-9961"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Congying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5140197473","display_name":"Jin Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Jin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.7889999747276306,"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":0.7889999747276306,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.08560000360012054,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.028300000354647636,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/barotropic-fluid","display_name":"Barotropic fluid","score":0.7440999746322632},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6879000067710876},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6468999981880188},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6144999861717224},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.44920000433921814},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4465999901294708},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.42750000953674316},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.3804999887943268}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7497000098228455},{"id":"https://openalex.org/C29712183","wikidata":"https://www.wikidata.org/wiki/Q739293","display_name":"Barotropic fluid","level":2,"score":0.7440999746322632},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6879000067710876},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6144999861717224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.550000011920929},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41609999537467957},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.3804999887943268},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.31690001487731934},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.2711000144481659},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.05105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.05105","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.05105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.05105","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,"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"},"sustainable_development_goals":[{"score":0.6595960259437561,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,46],"study":[1],"a":[2,30,37,57,87],"Marker-and-Cell":[3],"(MAC)":[4],"scheme":[5,27],"for":[6,92],"the":[7,14,22,25,54,65,70,73,78,93],"barotropic":[8],"Euler":[9],"system.":[10],"First,":[11],"we":[12,76,97],"apply":[13],"recently":[15],"developed":[16],"Lax-type":[17],"convergence":[18,23,88],"theorem":[19],"to":[20,28,53,86],"show":[21],"of":[24,56,64,72,83,90],"MAC":[26],"i)":[29],"dissipative":[31],"weak":[32],"solution":[33,39],"unconditionally":[34],"and":[35],"ii)":[36],"strong":[38,58],"as":[40,42],"long":[41],"it":[43],"exists.":[44],"Second,":[45],"derive":[47],"relative":[48,80],"energy":[49,81],"error":[50],"estimates":[51],"up":[52],"lifespan":[55],"solution,":[59],"without":[60],"assuming":[61,69],"uniform":[62],"boundedness":[63,71],"numerical":[66,74,94,103],"sequence.":[67],"Additionally,":[68],"solutions,":[75],"obtain":[77],"optimal":[79],"rate":[82,89],"1,":[84],"corresponding":[85],"1/2":[91],"solutions.":[95],"Finally,":[96],"corroborate":[98],"our":[99],"theoretical":[100],"results":[101],"by":[102],"experiments.":[104]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-08T00:00:00"}