{"id":"https://openalex.org/W4415370577","doi":"https://doi.org/10.3390/computation13100246","title":"Stability of the DuFort\u2013Frankel Scheme on Unstructured Grids","display_name":"Stability of the DuFort\u2013Frankel Scheme on Unstructured Grids","publication_year":2025,"publication_date":"2025-10-20","ids":{"openalex":"https://openalex.org/W4415370577","doi":"https://doi.org/10.3390/computation13100246"},"language":"en","primary_location":{"id":"doi:10.3390/computation13100246","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13100246","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/computation13100246","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021846283","display_name":"Nikolay Yavich","orcid":"https://orcid.org/0000-0002-8913-7710"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Nikolay Yavich","raw_affiliation_strings":["AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia"],"raw_orcid":"https://orcid.org/0000-0002-8913-7710","affiliations":[{"raw_affiliation_string":"AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia","institution_ids":["https://openalex.org/I125989756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088950452","display_name":"Evgeny Burnaev","orcid":"https://orcid.org/0000-0001-8424-0690"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Evgeny Burnaev","raw_affiliation_strings":["AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia","Autonomous Non-Profit Organization Artificial Intelligence Research Institute (AIRI), Moscow 105064, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia","institution_ids":["https://openalex.org/I125989756"]},{"raw_affiliation_string":"Autonomous Non-Profit Organization Artificial Intelligence Research Institute (AIRI), Moscow 105064, Russia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086058139","display_name":"Vladimir Vanovskiy","orcid":"https://orcid.org/0000-0003-3317-9572"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir Vanovskiy","raw_affiliation_strings":["AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia"],"raw_orcid":"https://orcid.org/0000-0003-3317-9572","affiliations":[{"raw_affiliation_string":"AI Center, Skolkovo Institute of Science and Technology, Moscow 121205, Russia","institution_ids":["https://openalex.org/I125989756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021846283"],"corresponding_institution_ids":["https://openalex.org/I125989756"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.37,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89971965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"13","issue":"10","first_page":"246","last_page":"246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9850000143051147,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9850000143051147,"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":0.9605000019073486,"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":0.925000011920929,"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/stability","display_name":"Stability (learning theory)","score":0.7287999987602234},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6991000175476074},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.656000018119812},{"id":"https://openalex.org/keywords/unstructured-grid","display_name":"Unstructured grid","score":0.607699990272522},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6007999777793884},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.5681999921798706},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.48350000381469727},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.48330000042915344},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.47360000014305115}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7287999987602234},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6991000175476074},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.656000018119812},{"id":"https://openalex.org/C134620963","wikidata":"https://www.wikidata.org/wiki/Q17078677","display_name":"Unstructured grid","level":3,"score":0.607699990272522},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6007999777793884},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.5681999921798706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5239999890327454},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.48330000042915344},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.47360000014305115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41780000925064087},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4090999960899353},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38370001316070557},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3246000111103058},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2971999943256378},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2955999970436096},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C196031653","wikidata":"https://www.wikidata.org/wiki/Q1501867","display_name":"Cartographic generalization","level":3,"score":0.2623000144958496},{"id":"https://openalex.org/C3018572313","wikidata":"https://www.wikidata.org/wiki/Q1256511","display_name":"Grid pattern","level":3,"score":0.26100000739097595},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation13100246","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13100246","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b1dd749cd8dd4e5db7ffbb23ed58484a","is_oa":true,"landing_page_url":"https://doaj.org/article/b1dd749cd8dd4e5db7ffbb23ed58484a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 13, Iss 10, p 246 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation13100246","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13100246","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7953343303","display_name":null,"funder_award_id":"24-41-02035","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1483728884","https://openalex.org/W1549748890","https://openalex.org/W1966775587","https://openalex.org/W1999948293","https://openalex.org/W2005510869","https://openalex.org/W2015221450","https://openalex.org/W2025353468","https://openalex.org/W2047450102","https://openalex.org/W2073339836","https://openalex.org/W2115894759","https://openalex.org/W2118678783","https://openalex.org/W2146156948","https://openalex.org/W2963157298","https://openalex.org/W3113378505","https://openalex.org/W3131026021","https://openalex.org/W4253494518","https://openalex.org/W4297471043","https://openalex.org/W4378800517"],"related_works":[],"abstract_inverted_index":{"The":[0],"DuFort\u2013Frankel":[1,48],"scheme":[2,49],"was":[3],"introduced":[4],"in":[5,64],"the":[6,47,71,88,91,94],"1950s":[7],"to":[8,20,36,54],"solve":[9],"parabolic":[10],"equations,":[11],"and":[12,23,67,69],"has":[13,33],"been":[14,34],"widely":[15],"used":[16],"ever":[17],"since":[18],"due":[19],"its":[21,31,84],"stability":[22,85],"explicit":[24],"nature.":[25],"However,":[26],"for":[27,75],"over":[28],"seven":[29],"decades,":[30],"application":[32],"limited":[35],"Cartesian":[37],"grids.":[38,57],"In":[39],"this":[40],"work,":[41],"we":[42,59,79],"propose":[43],"a":[44,81],"generalization":[45],"of":[46,83,90,93],"that":[50],"could":[51],"be":[52],"applied":[53],"arbitrary":[55],"unstructured":[56],"Specifically,":[58],"focus":[60],"on":[61,87],"Voronoi":[62],"grids":[63],"both":[65],"2D":[66],"3D,":[68],"use":[70],"finite":[72],"volume":[73],"method":[74],"spatial":[76],"discretization.":[77],"Additionally,":[78],"present":[80],"proof":[82],"based":[86],"analysis":[89],"spectrum":[92],"amplification":[95],"matrix,":[96],"along":[97],"with":[98],"numerical":[99],"examples.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-21T00:00:00"}