{"id":"https://openalex.org/W7159044149","doi":"https://doi.org/10.48550/arxiv.2604.26336","title":"A Second-Order Maximum-Principle-Preserving Crouzeix-Raviart Finite Element Method for Time-dependent Transport Equation","display_name":"A Second-Order Maximum-Principle-Preserving Crouzeix-Raviart Finite Element Method for Time-dependent Transport Equation","publication_year":2026,"publication_date":"2026-04-29","ids":{"openalex":"https://openalex.org/W7159044149","doi":"https://doi.org/10.48550/arxiv.2604.26336"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.26336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26336","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2604.26336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042341009","display_name":"Shipeng Mao","orcid":"https://orcid.org/0000-0003-4115-6039"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mao, Shipeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134891192","display_name":"Mingyang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Mingyang","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9477999806404114,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9477999806404114,"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":0.012000000104308128,"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/T11416","display_name":"Numerical methods for differential equations","score":0.00839999970048666,"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/finite-element-method","display_name":"Finite element method","score":0.6593999862670898},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5609999895095825},{"id":"https://openalex.org/keywords/solenoidal-vector-field","display_name":"Solenoidal vector field","score":0.5184000134468079},{"id":"https://openalex.org/keywords/mass-matrix","display_name":"Mass matrix","score":0.5083000063896179},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.47209998965263367},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4691999852657318},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4641999900341034},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44699999690055847},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.42179998755455017},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.40689998865127563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7215999960899353},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6593999862670898},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5609999895095825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5322999954223633},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.5184000134468079},{"id":"https://openalex.org/C135585149","wikidata":"https://www.wikidata.org/wiki/Q339704","display_name":"Mass matrix","level":3,"score":0.5083000063896179},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.47209998965263367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4706000089645386},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4691999852657318},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44699999690055847},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.40689998865127563},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.373199999332428},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.3643999993801117},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.33059999346733093},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C48395688","wikidata":"https://www.wikidata.org/wiki/Q6823714","display_name":"Method of fundamental solutions","level":5,"score":0.26170000433921814},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.251800000667572},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2500999867916107},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.26336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26336","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2604.26336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.26336","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,104],"this":[1],"paper,":[2],"we":[3,97,106],"construct":[4,56],"an":[5],"explicit,":[6],"second-order,":[7],"and":[8,53,77,80,89,148,155,162],"maximum-principle-preserving":[9],"Crouzeix-Raviart":[10],"(CR)":[11],"finite":[12],"element":[13,31],"method":[14],"for":[15,49],"two-dimensional":[16],"time-dependent":[17],"transport":[18,91],"equation.":[19],"The":[20],"key":[21],"observation":[22],"is":[23,32],"that":[24,60,125],"the":[25,29,41,62,123,127,131,138,160,165],"mass":[26],"matrix":[27],"of":[28,87,164],"CR":[30],"with":[33,152],"diagonal":[34],"structure,":[35],"which":[36],"allows":[37],"us":[38],"to":[39,43,55,115],"avoid":[40],"need":[42],"solve":[44],"a":[45,57,66,100,108,117],"large":[46],"linear":[47,120],"system":[48],"each":[50],"time":[51],"step":[52],"help":[54],"low-order":[58,72],"scheme":[59],"preserves":[61],"maximum":[63,128],"principle":[64,129],"in":[65],"simple":[67,109],"way.":[68],"We":[69],"first":[70],"introduce":[71],"schemes":[73,140],"based":[74,111],"on":[75,112,122,130,145],"minimum":[76],"bilinear":[78],"viscosities,":[79],"then":[81],"recover":[82],"second-order":[83],"accuracy":[84,161],"by":[85],"means":[86],"greedy":[88],"flux-corrected":[90],"viscosities.":[92],"For":[93],"inflow":[94],"boundary":[95],"conditions,":[96],"further":[98],"design":[99],"modified":[101],"FCT":[102],"limiter.":[103],"addition,":[105],"propose":[107],"reconstruction":[110],"Wachspress":[113],"coordinates":[114],"obtain":[116],"continuous":[118],"piecewise":[119],"approximation":[121],"$\\frac{h}2$-mesh":[124],"satisfies":[126],"whole":[132],"domain.":[133],"Under":[134],"divergence-free":[135],"velocity":[136,157],"fields,":[137,158],"proposed":[139,166],"are":[141],"conservative.":[142],"Numerical":[143],"experiments":[144],"both":[146,153],"smooth":[147],"discontinuous":[149],"test":[150],"cases,":[151],"solenoidal":[154],"non-solenoidal":[156],"confirm":[159],"robustness":[163],"schemes.":[167]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-01T00:00:00"}
