{"id":"https://openalex.org/W7214722835","doi":"https://doi.org/10.48550/arxiv.2609.33201","title":"The stability barrier of a class of Hermite-type discretizations of advection equations","display_name":"The stability barrier of a class of Hermite-type discretizations of advection equations","publication_year":2026,"publication_date":"2026-09-27","ids":{"openalex":"https://openalex.org/W7214722835","doi":"https://doi.org/10.48550/arxiv.2609.33201"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.33201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33201","pdf_url":"https://arxiv.org/pdf/2609.33201","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/2609.33201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153456582","display_name":"Xianyi Zeng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zeng, Xianyi","raw_affiliation_strings":["Department of Mathematics , Lehigh University , Bethlehem , PA 18015 , United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Lehigh University , Bethlehem , PA 18015 , United States","institution_ids":["https://openalex.org/I186143895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5153456582"],"corresponding_institution_ids":["https://openalex.org/I186143895"],"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":0.6431000232696533,"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":0.6431000232696533,"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":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.21439999341964722,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.11959999799728394,"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/linear-advection-equation","display_name":"linear advection equation","score":0.8059999942779541},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.7229999899864197},{"id":"https://openalex.org/keywords/upwind-schemes","display_name":"upwind schemes","score":0.6119999885559082},{"id":"https://openalex.org/keywords/central-schemes","display_name":"central schemes","score":0.8759999871253967},{"id":"https://openalex.org/keywords/marginal-stability","display_name":"marginal stability","score":0.8759999871253967},{"id":"https://openalex.org/keywords/sign-changing-solutions","display_name":"sign-changing solutions","score":0.8989999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944999933242798},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7070000171661377},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6870999932289124},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5608999729156494},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.5217000246047974},{"id":"https://openalex.org/C76752949","wikidata":"https://www.wikidata.org/wiki/Q7607499","display_name":"Stencil","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5078999996185303},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4952000081539154},{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.4862000048160553},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48539999127388},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.32899999618530273},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.31850001215934753},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C43466630","wikidata":"https://www.wikidata.org/wiki/Q17098945","display_name":"Linear stability","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.263700008392334},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.33201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33201","pdf_url":"https://arxiv.org/pdf/2609.33201","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.2609.33201","doi":"https://doi.org/10.48550/arxiv.2609.33201","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.33201","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:2609.33201","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.33201","pdf_url":"https://arxiv.org/pdf/2609.33201","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/W7214722835.pdf","grobid_xml":"https://content.openalex.org/works/W7214722835.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4417106610","https://openalex.org/W7213284369","https://openalex.org/W2900235489","https://openalex.org/W2052912148","https://openalex.org/W2080472131","https://openalex.org/W2509529717","https://openalex.org/W2149712123","https://openalex.org/W4306181147","https://openalex.org/W1971897106","https://openalex.org/W2558336603"],"abstract_inverted_index":{"In":[0,27],"this":[1],"paper":[2],"we":[3,32],"fully":[4],"categorize":[5],"all":[6,120,140],"hybrid-variable":[7],"(HV)":[8],"discretizations":[9],"of":[10,24,85,133],"linear":[11],"advection":[12],"equations":[13],"according":[14],"to":[15,36],"their":[16],"stability":[17,22,58],"property":[18],"and":[19,40,43,74,112],"establish":[20],"the":[21,28,52,61,67,83,88,95,107,128,131,134],"barrier":[23,59],"these":[25],"methods.":[26],"HV":[29,53,69,122],"discretization":[30],"framework,":[31],"find":[33],"numerical":[34,149],"approximations":[35],"both":[37],"cell-averaged":[38],"solutions":[39,42],"nodal":[41],"evolve":[44],"them":[45],"in":[46,87,94,127],"time":[47],"simultaneously.":[48],"We":[49],"prove":[50],"that":[51,66,82,93,119,130],"methods":[54],"have":[55],"a":[56,79],"similar":[57],"as":[60],"classical":[62],"finite":[63],"difference":[64],"schemes,":[65],"semi-discretized":[68],"scheme":[70],"is":[71,91,116],"stable":[72],"if":[73,76],"only":[75,103],"it":[77],"uses":[78],"stencil":[80],"such":[81],"number":[84],"unknowns":[86],"upwind":[89],"direction":[90,97],"precisely":[92],"downwind":[96],"plus":[98],"one":[99,104],"or":[100],"two,":[101],"with":[102],"exception":[105],"when":[106],"two":[108],"numbers":[109],"are":[110,124,145],"three":[111],"zero,":[113],"respectively.":[114],"It":[115],"also":[117],"proved":[118],"central":[121],"schemes":[123],"neutrally":[125],"stable,":[126],"sense":[129],"L2-norm":[132],"solution":[135],"remain":[136],"uniformly":[137],"bounded":[138],"at":[139],"times.":[141],"The":[142],"theoretical":[143],"predictions":[144],"verify":[146],"by":[147],"extensive":[148],"tests.":[150]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-30T00:00:00"}
