{"id":"https://openalex.org/W1983493416","doi":"https://doi.org/10.1137/07068237x","title":"An A Posteriori\u2013A Priori Analysis of Multiscale Operator Splitting","display_name":"An A Posteriori\u2013A Priori Analysis of Multiscale Operator Splitting","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1983493416","doi":"https://doi.org/10.1137/07068237x","mag":"1983493416"},"language":"en","primary_location":{"id":"doi:10.1137/07068237x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068237x","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/A5036663902","display_name":"D. Estep","orcid":null},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Estep","raw_affiliation_strings":["COLORADO STATE UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"COLORADO STATE UNIVERSITY","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032561283","display_name":"Victor Ginting","orcid":"https://orcid.org/0000-0002-8191-5944"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"V. Ginting","raw_affiliation_strings":["COLORADO STATE UNIVERSITY"],"affiliations":[{"raw_affiliation_string":"COLORADO STATE UNIVERSITY","institution_ids":["https://openalex.org/I92446798"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075736466","display_name":"David L. Ropp","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Ropp","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018004800","display_name":"John N. Shadid","orcid":"https://orcid.org/0009-0001-9804-1649"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. N. Shadid","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017115099","display_name":"Simon Tavener","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Tavener","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036663902"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"apc_list":null,"apc_paid":null,"fwci":4.5275,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.94122408,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"3","first_page":"1116","last_page":"1146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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":0.9977999925613403,"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/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.8142210245132446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7722803354263306},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7707985639572144},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6504195332527161},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5858156681060791},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5819776654243469},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5237084031105042},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.47507065534591675},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4700440466403961},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.45341596007347107},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4269983768463135},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34349119663238525},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.23101836442947388}],"concepts":[{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.8142210245132446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7722803354263306},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7707985639572144},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6504195332527161},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5858156681060791},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5819776654243469},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5237084031105042},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.47507065534591675},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4700440466403961},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.45341596007347107},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4269983768463135},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34349119663238525},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.23101836442947388},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/07068237x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068237x","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.119.6050","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.119.6050","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.colostate.edu/~estep/research/preprints/oprsplit.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.395.5134","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.395.5134","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.colostate.edu/~tavener/manuscripts/ginting/os-2008.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W40078647","https://openalex.org/W140544284","https://openalex.org/W1593553932","https://openalex.org/W1902819800","https://openalex.org/W1963942260","https://openalex.org/W1970564105","https://openalex.org/W1974477559","https://openalex.org/W1979156898","https://openalex.org/W1984257336","https://openalex.org/W1993325724","https://openalex.org/W1995183446","https://openalex.org/W2001405518","https://openalex.org/W2008166083","https://openalex.org/W2038991247","https://openalex.org/W2041523977","https://openalex.org/W2044355921","https://openalex.org/W2049161806","https://openalex.org/W2055946379","https://openalex.org/W2062326781","https://openalex.org/W2062951693","https://openalex.org/W2078851442","https://openalex.org/W2081416965","https://openalex.org/W2081995212","https://openalex.org/W2092910485","https://openalex.org/W2124274248","https://openalex.org/W2136919854","https://openalex.org/W2140505128","https://openalex.org/W2148639620","https://openalex.org/W2519750562","https://openalex.org/W2619278502","https://openalex.org/W2751889903","https://openalex.org/W3021722416","https://openalex.org/W4231288452","https://openalex.org/W4235725823"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2162026849","https://openalex.org/W2394687667"],"abstract_inverted_index":{"In":[0,153],"this":[1,155],"paper,":[2],"we":[3],"analyze":[4,33],"a":[5,26,60,65,70,112,114,120,124,144],"multiscale":[6,53,145],"operator":[7,54,77,93,146,167],"splitting":[8,78,94,147],"method":[9],"for":[10,75,139],"solving":[11],"systems":[12],"of":[13,25,39,46,68,91,98,101,111],"ordinary":[14],"differential":[15],"equations":[16],"such":[17],"as":[18],"those":[19],"that":[20,49,135,163],"result":[21,51],"upon":[22],"space":[23],"discretization":[24,97,148],"reaction-diffusion":[27],"equation.":[28],"Our":[29],"goal":[30],"is":[31],"to":[32,159],"and":[34,64,95,119,143],"accurately":[35],"estimate":[36],"the":[37,40,44,89,92,96,102,109,133,136,140,157],"error":[38,62,73],"numerical":[41],"solution,":[42],"including":[43],"effects":[45,90],"any":[47],"instabilities":[48,162],"can":[50,164],"from":[52,166],"splitting.":[55,168],"We":[56],"present":[57],"both":[58],"an":[59,76],"priori":[61,125],"analysis":[63,74,107,129],"new":[66],"type":[67],"hybrid":[69,106,128],"priori\u2013a":[71],"posteriori":[72,115],"discontinuous":[79],"Galerkin":[80],"finite":[81],"element":[82],"method.":[83],"Both":[84],"analyses":[85],"clearly":[86],"distinguish":[87],"between":[88],"each":[99],"component":[100],"decomposed":[103],"problem.":[104],"The":[105,127],"has":[108],"form":[110],"computable":[113],"leading":[116],"order":[117,123],"expression":[118],"provably":[121],"higher":[122],"expression.":[126],"takes":[130],"into":[131],"account":[132],"fact":[134],"adjoint":[137],"problems":[138],"original":[141],"problem":[142],"differ":[149],"in":[150],"significant":[151],"ways.":[152],"particular,":[154],"provides":[156],"means":[158],"monitor":[160],"global":[161],"arise":[165]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}