{"id":"https://openalex.org/W2608555450","doi":"https://doi.org/10.1137/16m1092763","title":"Fully Computable Error Estimation of a Nonlinear, Positivity-Preserving Discretization of the Convection-Diffusion-Reaction Equation","display_name":"Fully Computable Error Estimation of a Nonlinear, Positivity-Preserving Discretization of the Convection-Diffusion-Reaction Equation","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2608555450","doi":"https://doi.org/10.1137/16m1092763","mag":"2608555450"},"language":"en","primary_location":{"id":"doi:10.1137/16m1092763","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1092763","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5015733916","display_name":"Alejandro Allendes","orcid":"https://orcid.org/0000-0002-3305-6823"},"institutions":[{"id":"https://openalex.org/I75778554","display_name":"Federico Santa Mar\u00eda Technical University","ror":"https://ror.org/05510vn56","country_code":"CL","type":"education","lineage":["https://openalex.org/I75778554"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Alejandro Allendes","raw_affiliation_strings":["AM2V and Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile"],"affiliations":[{"raw_affiliation_string":"AM2V and Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile","institution_ids":["https://openalex.org/I75778554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025324947","display_name":"Gabriel R. Barrenechea","orcid":"https://orcid.org/0000-0003-4490-678X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gabriel R. Barrenechea","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016647975","display_name":"Richard Rankin","orcid":"https://orcid.org/0000-0001-6445-2602"},"institutions":[{"id":"https://openalex.org/I75778554","display_name":"Federico Santa Mar\u00eda Technical University","ror":"https://ror.org/05510vn56","country_code":"CL","type":"education","lineage":["https://openalex.org/I75778554"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Richard Rankin","raw_affiliation_strings":["AM2V and Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile"],"affiliations":[{"raw_affiliation_string":"AM2V and Departamento de Matem\u00e1tica, Universidad T\u00e9cnica Federico Santa Mar\u00eda, Valpara\u00edso, Chile","institution_ids":["https://openalex.org/I75778554"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015733916"],"corresponding_institution_ids":["https://openalex.org/I75778554"],"apc_list":null,"apc_paid":null,"fwci":0.7407,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.68402689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"5","first_page":"A1903","last_page":"A1927"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8284444808959961},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8038390278816223},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.713605523109436},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6722295880317688},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6442917585372925},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5875754356384277},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5757021307945251},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5669644474983215},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5104750394821167},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4843357801437378},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43633517622947693},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32489773631095886},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06133201718330383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8284444808959961},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8038390278816223},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.713605523109436},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6722295880317688},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6442917585372925},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5875754356384277},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5757021307945251},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5669644474983215},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5104750394821167},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4843357801437378},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43633517622947693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32489773631095886},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06133201718330383},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1092763","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1092763","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:strathprints.strath.ac.uk:60427","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/view/author/566211.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1312887395","display_name":null,"funder_award_id":"BASAL PFB03 CMM","funder_id":"https://openalex.org/F4320323458","funder_display_name":"Universidad de Chile"},{"id":"https://openalex.org/G341900282","display_name":null,"funder_award_id":"116.12.1","funder_id":"https://openalex.org/F4320310976","funder_display_name":"Universidad T\u00e9cnica Federico Santa Mar\u00eda"},{"id":"https://openalex.org/G81652787","display_name":null,"funder_award_id":"MEC 80140118","funder_id":"https://openalex.org/F4320334812","funder_display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica"}],"funders":[{"id":"https://openalex.org/F4320310976","display_name":"Universidad T\u00e9cnica Federico Santa Mar\u00eda","ror":"https://ror.org/05510vn56"},{"id":"https://openalex.org/F4320323458","display_name":"Universidad de Chile","ror":"https://ror.org/047gc3g35"},{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1800104704","https://openalex.org/W1973166496","https://openalex.org/W1975480806","https://openalex.org/W1985933103","https://openalex.org/W1986669237","https://openalex.org/W1987971235","https://openalex.org/W2003116365","https://openalex.org/W2007322777","https://openalex.org/W2012884947","https://openalex.org/W2016535570","https://openalex.org/W2034290095","https://openalex.org/W2044335108","https://openalex.org/W2063214641","https://openalex.org/W2064201813","https://openalex.org/W2070299075","https://openalex.org/W2071202306","https://openalex.org/W2085476229","https://openalex.org/W2086654907","https://openalex.org/W2087270837","https://openalex.org/W2090061427","https://openalex.org/W2092071033","https://openalex.org/W2123897417","https://openalex.org/W2152799582","https://openalex.org/W2155369712","https://openalex.org/W2236644215","https://openalex.org/W2258665993","https://openalex.org/W2519971170","https://openalex.org/W2576243093","https://openalex.org/W2749486094","https://openalex.org/W2963139945"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W3185235544","https://openalex.org/W2364741597","https://openalex.org/W4297791327","https://openalex.org/W4387559320","https://openalex.org/W2019529034","https://openalex.org/W828409841","https://openalex.org/W4388482258","https://openalex.org/W4293683879","https://openalex.org/W1982328599"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,35,85,94,113],"devoted":[3],"to":[4,96],"the":[5,26,43,47,55,72,75,78,82,92,111],"proposal,":[6],"analysis,":[7],"and":[8,89,110,121],"numerical":[9,117],"testing":[10],"of":[11,22,25,31,45,74,103],"a":[12,15,20,61,67],"fully":[13],"computable":[14],"posteriori":[16,62],"error":[17,63],"bound":[18,70],"for":[19],"class":[21],"nonlinear":[23],"discretizations":[24,104],"convection-diffusion-reaction":[27],"equation.":[28],"The":[29],"type":[30],"discretization":[32],"we":[33,58],"consider":[34],"nonlinear,":[36],"since":[37],"it":[38],"has":[39],"been":[40],"built":[41],"with":[42],"aim":[44],"preserving":[46],"discrete":[48],"maximum":[49],"principle.":[50],"Under":[51,77],"mild":[52],"assumptions":[53],"on":[54,71],"stabilizing":[56,83],"term,":[57],"obtain":[59],"an":[60],"estimator":[64,93],"that":[65,81,105],"provides":[66],"certified":[68],"upper":[69],"norm":[73],"error.":[76],"additional":[79],"assumption":[80],"term":[84],"both":[86],"Lipschitz":[87],"continuous":[88],"linearity":[90],"preserving,":[91],"shown":[95],"be":[97],"locally":[98],"efficient.":[99],"We":[100],"present":[101],"examples":[102],"satisfy":[106],"these":[107],"two":[108,120],"requirements,":[109],"theory":[112],"illustrated":[114],"by":[115],"several":[116],"experiments":[118],"in":[119],"three":[122],"space":[123],"dimensions.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
