{"id":"https://openalex.org/W7214033916","doi":"https://doi.org/10.48550/arxiv.2609.23546","title":"A novel monotonous finite volume element scheme for convection dominant diffusion problem","display_name":"A novel monotonous finite volume element scheme for convection dominant diffusion problem","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214033916","doi":"https://doi.org/10.48550/arxiv.2609.23546"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23546","pdf_url":"https://arxiv.org/pdf/2609.23546","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/2609.23546","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021311742","display_name":"Cunyun Nie","orcid":"https://orcid.org/0000-0002-8485-9722","observed_orcids":["https://orcid.org/0000-0002-8485-9722"]},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nie, Cunyun","raw_affiliation_strings":[". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152467701","display_name":"Xiaoling Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Xiaoling","raw_affiliation_strings":[". School of Future Technology , Hunan Institute of Engineering , 411104 , Hunan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Future Technology , Hunan Institute of Engineering , 411104 , Hunan , China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100717507","display_name":"Zhujun Wang","orcid":"https://orcid.org/0000-0003-0503-9687","observed_orcids":["https://orcid.org/0000-0003-0503-9687"]},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"wang, Zhujun","raw_affiliation_strings":[". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071273939","display_name":"Zhikun Tian","orcid":"https://orcid.org/0000-0003-3668-112X","observed_orcids":["https://orcid.org/0000-0003-3668-112X"]},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tian, Zhikun","raw_affiliation_strings":[". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China","institution_ids":["https://openalex.org/I27688046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152472617","display_name":"Chengjie Xia","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27688046","display_name":"Hunan Institute of Engineering","ror":"https://ror.org/03zj2rn70","country_code":"CN","type":"education","lineage":["https://openalex.org/I27688046"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xia, Chengjie","raw_affiliation_strings":[". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Computational Science and Electronics , Hunan Institute of Engineering , 411104 , Hunan , China","institution_ids":["https://openalex.org/I27688046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27688046"],"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9940999746322632,"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":0.9940999746322632,"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":0.0052999998442828655,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00019999999494757503,"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/convection-dominated-diffusion","display_name":"convection-dominated diffusion","score":0.972000002861023},{"id":"https://openalex.org/keywords/error-estimation","display_name":"error estimation","score":0.6119999885559082},{"id":"https://openalex.org/keywords/l2-error-estimates","display_name":"L2 error estimates","score":0.734000027179718}],"concepts":[{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.7986000180244446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7307000160217285},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.6916999816894531},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5705000162124634},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5649999976158142},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5590000152587891},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3982999920845032},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3725999891757965},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.35740000009536743},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C101303905","wikidata":"https://www.wikidata.org/wiki/Q17104838","display_name":"Numerical solution of the convection\u2013diffusion equation","level":4,"score":0.32109999656677246},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3077000081539154},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C85405225","wikidata":"https://www.wikidata.org/wiki/Q17013617","display_name":"Finite volume method for one-dimensional steady state diffusion","level":4,"score":0.27570000290870667},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.27459999918937683},{"id":"https://openalex.org/C148444096","wikidata":"https://www.wikidata.org/wiki/Q7069655","display_name":"Numerical diffusion","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.2696000039577484}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23546","pdf_url":"https://arxiv.org/pdf/2609.23546","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.2609.23546","doi":"https://doi.org/10.48550/arxiv.2609.23546","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23546","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:2609.23546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23546","pdf_url":"https://arxiv.org/pdf/2609.23546","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/W7214033916.pdf","grobid_xml":"https://content.openalex.org/works/W7214033916.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214734228","https://openalex.org/W1910626420","https://openalex.org/W2911527859","https://openalex.org/W2376864571","https://openalex.org/W2999035954","https://openalex.org/W2032941119","https://openalex.org/W4281809868","https://openalex.org/W7212566192","https://openalex.org/W2147816048","https://openalex.org/W7098581735"],"abstract_inverted_index":{"One":[0],"novel":[1,146],"monotonous":[2],"finite":[3,82,166],"volume":[4,83,167],"element":[5,94,168],"(MFVE)":[6],"scheme":[7],"is":[8,33,67,77,98,115,156,183],"put":[9,134],"forward":[10],"for":[11,35,59,111,158],"convection":[12,40,61,113],"dominant":[13],"diffusion":[14,160],"problem.":[15],"The":[16,173],"main":[17],"contributions":[18],"of":[19,38,88,95,124,176,179],"this":[20],"paper":[21],"include":[22],"four":[23],"aspects.":[24],"Firstly,":[25],"one":[26,54,85,101,106,145,164],"upwind":[27,31,45,51,74],"sub-control":[28],"volume,":[29,32,75],"called":[30],"introduced":[34],"the":[36,39,44,50,60,64,80,92,112,118,136,177,180],"discretization":[37],"term":[41,62,114],"similar":[42],"to":[43,49],"element,":[46],"which":[47,76,138],"leads":[48],"property.":[52],"Secondly,":[53],"first-order":[55],"linear":[56],"discrete":[57,109,170],"operator":[58,110],"in":[63,73,91],"balance":[65],"equation":[66],"directly":[68],"obtained":[69],"by":[70,100,117,152],"numerical":[71,186],"integration":[72],"different":[78],"from":[79],"classical":[81],"methods.Thirdly,":[84],"asymptotic":[86,119],"expansion":[87,120],"gradient":[89],"functions":[90],"dual":[93],"each":[96],"node":[97],"derived":[99],"extension":[102],"interpolation":[103],"function.":[104],"Then,":[105],"second-order":[107],"nonlinear":[108],"constructed":[116],"and":[121],"error":[122,178],"estimation":[123],"its":[125],"FVE":[126],"solution,":[127],"where":[128],"some":[129],"perturbed":[130],"coefficients":[131],"are":[132],"skillfully":[133],"into":[135],"expansion,":[137],"serves":[139],"as":[140],"a":[141],"high-order":[142],"correction.":[143],"Fourthly,":[144],"two-order":[147],"MFVE":[148],"scheme,":[149],"also":[150],"accompanied":[151],"another":[153],"one-order":[154],"MFVE,":[155],"designed":[157],"convection-dominated":[159],"problems":[161],"together":[162],"with":[163],"positivity-preserving":[165],"(PFVE)":[169],"diffusive":[171],"operator.":[172],"L2":[174],"norm":[175],"approximate":[181],"solution":[182],"derived.":[184],"Finally,":[185],"results":[187],"validate":[188],"theoretical":[189],"conclusions.":[190]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-23T00:00:00"}
