{"id":"https://openalex.org/W4385617834","doi":"https://doi.org/10.1515/cmam-2023-0009","title":"A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System","display_name":"A Convergent Entropy-Dissipating BDF2 Finite-Volume Scheme for a Population Cross-Diffusion System","publication_year":2023,"publication_date":"2023-08-07","ids":{"openalex":"https://openalex.org/W4385617834","doi":"https://doi.org/10.1515/cmam-2023-0009"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2023-0009","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0009","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084423759","display_name":"Ansgar J\u00fcngel","orcid":"https://orcid.org/0000-0003-0633-8929"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Ansgar J\u00fcngel","raw_affiliation_strings":["Institute of Analysis and Scientific Computing , Technische Universit\u00e4t Wien , Wiedner Hauptstra\u00dfe 8\u201310, 1040 Wien , Austria"],"raw_orcid":"https://orcid.org/0000-0003-0633-8929","affiliations":[{"raw_affiliation_string":"Institute of Analysis and Scientific Computing , Technische Universit\u00e4t Wien , Wiedner Hauptstra\u00dfe 8\u201310, 1040 Wien , Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006213811","display_name":"Martin Vetter","orcid":"https://orcid.org/0009-0009-8552-0366"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Martin Vetter","raw_affiliation_strings":["Institute of Analysis and Scientific Computing , Technische Universit\u00e4t Wien , Wiedner Hauptstra\u00dfe 8\u201310, 1040 Wien , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Analysis and Scientific Computing , Technische Universit\u00e4t Wien , Wiedner Hauptstra\u00dfe 8\u201310, 1040 Wien , Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084423759"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":0.5552,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6960791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"24","issue":"3","first_page":"725","last_page":"746"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.978600025177002,"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/mathematics","display_name":"Mathematics","score":0.89231276512146},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7051013708114624},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6009156107902527},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.5978752374649048},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5682211518287659},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4626380503177643},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4272765517234802},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.41942083835601807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.366136372089386}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.89231276512146},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7051013708114624},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6009156107902527},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.5978752374649048},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5682211518287659},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4626380503177643},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4272765517234802},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41942083835601807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.366136372089386},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2023-0009","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2023-0009","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G1923426151","display_name":"Emerging Network Structures and Neuromorphic Applications","funder_award_id":"101018153","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G2568532592","display_name":"Taming Complexity in Partial Differential Systems","funder_award_id":"F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3155600227","display_name":"Multicomponent systems with incomplete diffusion","funder_award_id":"P33010","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1487310864","https://openalex.org/W1523793067","https://openalex.org/W1549748890","https://openalex.org/W1967804648","https://openalex.org/W1968435119","https://openalex.org/W1971738560","https://openalex.org/W1991670087","https://openalex.org/W2045332748","https://openalex.org/W2046173108","https://openalex.org/W2059769570","https://openalex.org/W2060452322","https://openalex.org/W2092009076","https://openalex.org/W2119877548","https://openalex.org/W2129802470","https://openalex.org/W2131955910","https://openalex.org/W2317911782","https://openalex.org/W2533536025","https://openalex.org/W2618767132","https://openalex.org/W2896095964","https://openalex.org/W2902036597","https://openalex.org/W2962845679","https://openalex.org/W2963236482","https://openalex.org/W2963783946","https://openalex.org/W2963946555","https://openalex.org/W2990399043","https://openalex.org/W3003241673","https://openalex.org/W3009234482","https://openalex.org/W3015453200","https://openalex.org/W3088726828","https://openalex.org/W3098765149","https://openalex.org/W3106268064","https://openalex.org/W3156195975","https://openalex.org/W4206619878"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2231544277"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"second-order":[2],"backward":[3],"differentiation":[4],"formula":[5],"(BDF2)":[6],"finite-volume":[7],"discretization":[8],"for":[9,68],"a":[10,76],"nonlinear":[11],"cross-diffusion":[12],"system":[13,89],"arising":[14],"in":[15,94],"population":[16],"dynamics":[17],"is":[18,81],"studied.":[19],"The":[20,32,53,79],"numerical":[21,92],"scheme":[22,50],"preserves":[23],"the":[24,30,46,49,58,61,69,82,88,101],"Rao":[25,71],"entropy":[26,72],"structure":[27],"and":[28,34,39,73,96],"conserves":[29],"mass.":[31],"existence":[33],"uniqueness":[35],"of":[36,48,60,84],"discrete":[37],"solutions":[38],"their":[40],"large-time":[41],"behavior":[42],"as":[43,45],"well":[44],"convergence":[47],"are":[51,55],"proved.":[52],"proofs":[54],"based":[56],"on":[57],"G-stability":[59],"BDF2":[62],"scheme,":[63],"which":[64],"provides":[65],"an":[66],"inequality":[67,86],"quadratic":[70],"hence":[74],"suitable":[75],"priori":[77],"estimates.":[78],"novelty":[80],"extension":[83],"this":[85],"to":[87],"case.":[90],"Some":[91],"experiments":[93],"one":[95],"two":[97],"space":[98],"dimensions":[99],"underline":[100],"theoretical":[102],"results.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}