{"id":"https://openalex.org/W3163403378","doi":"https://doi.org/10.1137/21m1421283","title":"Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance","display_name":"Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance","publication_year":2022,"publication_date":"2022-04-01","ids":{"openalex":"https://openalex.org/W3163403378","doi":"https://doi.org/10.1137/21m1421283","mag":"3163403378"},"language":"en","primary_location":{"id":"doi:10.1137/21m1421283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1421283","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5100373889","display_name":"Chun Liu","orcid":"https://orcid.org/0000-0002-0480-0107"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chun Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100417045","display_name":"Cheng Wang","orcid":"https://orcid.org/0000-0003-4220-8080"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100397311","display_name":"Yiwei Wang","orcid":"https://orcid.org/0000-0002-1267-9669"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yiwei Wang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028411348","display_name":"Steven M. Wise","orcid":"https://orcid.org/0000-0003-3824-2075"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steven M. Wise","raw_affiliation_strings":["University Of Tennessee"],"affiliations":[{"raw_affiliation_string":"University Of Tennessee","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100373889"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9079,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.9421847,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"60","issue":"2","first_page":"781","last_page":"803"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7147157192230225},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5751555562019348},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5659449696540833},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5473834872245789},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5337209701538086},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.519903838634491},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5100255608558655},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47813403606414795},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4279251992702484},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.42616862058639526},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35369783639907837},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10237091779708862},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10044637322425842}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7147157192230225},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5751555562019348},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5659449696540833},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5473834872245789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5337209701538086},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.519903838634491},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5100255608558655},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47813403606414795},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4279251992702484},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.42616862058639526},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35369783639907837},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10237091779708862},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10044637322425842},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1421283","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1421283","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6299999952316284,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2344081865","display_name":null,"funder_award_id":"DMS-1719854","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G244024126","display_name":null,"funder_award_id":"DMS-1950868","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4410185213","display_name":null,"funder_award_id":"DMS-2012669","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5592681154","display_name":null,"funder_award_id":"DMS-2012634","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7645898704","display_name":null,"funder_award_id":"DMS-1759536","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320313813","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W1496738390","https://openalex.org/W1509833722","https://openalex.org/W1605821011","https://openalex.org/W1973071367","https://openalex.org/W1973360544","https://openalex.org/W1974477559","https://openalex.org/W1991547299","https://openalex.org/W1999802587","https://openalex.org/W2002116790","https://openalex.org/W2003538236","https://openalex.org/W2006640177","https://openalex.org/W2008209583","https://openalex.org/W2012220122","https://openalex.org/W2013529907","https://openalex.org/W2020516618","https://openalex.org/W2023671338","https://openalex.org/W2025314501","https://openalex.org/W2031734874","https://openalex.org/W2036881253","https://openalex.org/W2037486322","https://openalex.org/W2041905900","https://openalex.org/W2061143699","https://openalex.org/W2072426122","https://openalex.org/W2074556087","https://openalex.org/W2076602180","https://openalex.org/W2078913341","https://openalex.org/W2083551379","https://openalex.org/W2092400970","https://openalex.org/W2103817893","https://openalex.org/W2118085053","https://openalex.org/W2121181367","https://openalex.org/W2121326637","https://openalex.org/W2168191634","https://openalex.org/W2171763495","https://openalex.org/W2172089016","https://openalex.org/W2185518952","https://openalex.org/W2285271170","https://openalex.org/W2322451921","https://openalex.org/W2587855701","https://openalex.org/W2592358629","https://openalex.org/W2608237429","https://openalex.org/W2747689913","https://openalex.org/W2750775214","https://openalex.org/W2755641349","https://openalex.org/W2963236482","https://openalex.org/W2963284241","https://openalex.org/W2981771356","https://openalex.org/W2992502473","https://openalex.org/W2997853869","https://openalex.org/W3003868259","https://openalex.org/W3008014436","https://openalex.org/W3015453200","https://openalex.org/W3098167548","https://openalex.org/W3098765149","https://openalex.org/W3103135100","https://openalex.org/W3123655821","https://openalex.org/W3133356548","https://openalex.org/W3135358591","https://openalex.org/W3141939412","https://openalex.org/W3157057017","https://openalex.org/W3157436598","https://openalex.org/W3158855716","https://openalex.org/W4244360209"],"related_works":["https://openalex.org/W2371200319","https://openalex.org/W2367609594","https://openalex.org/W2350320737","https://openalex.org/W2391455523","https://openalex.org/W2739518152","https://openalex.org/W2091416718","https://openalex.org/W2155484906","https://openalex.org/W2268131559","https://openalex.org/W4205231130","https://openalex.org/W4226416379"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,27,41,138,150,167,185,188,229,243],"detailed":[3,31,83],"convergence":[4,84,210,222,279],"analysis":[5,85,194,223,280],"for":[6,26,91,202,216],"an":[7,238],"operator":[8,93,204],"splitting":[9,94,205],"scheme":[10,35,73,215],"proposed":[11],"in":[12,47,54,98,117,157,161,208,266,283],"[C.":[13],"Liu,":[14],"C.":[15],"Wang,":[16,19],"and":[17,60,64,77,86,111,144,198,277],"Y.":[18],"J.":[20],"Comput.":[21],"Phys.,":[22],"436":[23],"(2021),":[24],"110253]":[25],"reaction-diffusion":[28,219],"system":[29],"with":[30],"balance.":[32],"The":[33,72,96,221],"numerical":[34,118,155,177,192,214,275],"has":[36],"been":[37],"constructed":[38],"based":[39],"on":[40,255],"recently":[42],"developed":[43],"energetic":[44],"variational":[45],"formulation,":[46],"which":[48,247],"the":[49,57,62,68,82,92,99,106,128,132,154,158,162,172,176,181,191,199,203,209,213,217,251,256,260,274,278],"reaction":[50,58,63,100,159,235,245,257,261],"part":[51],"is":[52,74,263],"reformulated":[53],"terms":[55,267],"of":[56,109,127,131,140,153,175,190,212,233,268],"trajectory,":[59],"both":[61],"diffusion":[65,182],"parts":[66],"dissipate":[67],"same":[69],"free":[70],"energy.":[71],"energy":[75],"stable":[76],"positivity-preserving.":[78],"In":[79,136],"this":[80,284],"paper,":[81],"error":[87,142,146,156,178,193],"estimate":[88,143,147,201,211],"are":[89],"performed":[90],"scheme.":[95],"nonlinearity":[97],"trajectory":[101],"equation,":[102],"as":[103,105],"well":[104],"implicit":[107],"treatment":[108],"nonlinear":[110,134],"singular":[112],"logarithmic":[113,133],"terms,":[114],"impose":[115],"challenges":[116],"analysis.":[119],"To":[120],"overcome":[121],"these":[122],"difficulties,":[123],"we":[124,240,271],"make":[125],"use":[126],"convex":[129],"nature":[130],"terms.":[135],"addition,":[137],"combination":[139,189],"rough":[141],"refined":[145],"leads":[148],"to":[149,228],"desired":[151],"bound":[152,174],"stage,":[160],"discrete":[163,168],"maximum":[164,169],"norm.":[165],"Furthermore,":[166],"principle":[170],"yields":[171],"evolution":[173],"function":[179],"at":[180,195],"stage.":[183],"As":[184,237],"direct":[186],"consequence,":[187],"different":[196],"stages":[197],"consistency":[200],"procedure":[206],"results":[207],"full":[218],"system.":[220],"technique":[224],"could":[225],"be":[226],"extended":[227],"more":[230,264],"general":[231],"class":[232],"dissipative":[234],"mechanisms.":[236],"example,":[239],"also":[241,281],"consider":[242],"near-equilibrium":[244],"kinetics,":[246],"was":[248],"derived":[249],"by":[250],"linear":[252],"response":[253],"assumption":[254],"trajectory.":[258],"Although":[259],"rate":[262],"complicated":[265],"concentration":[269],"variables,":[270],"show":[272],"that":[273],"approach":[276],"work":[282],"case.":[285]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}
