{"id":"https://openalex.org/W2184367770","doi":"https://doi.org/10.1137/15m1021982","title":"An Abstract Analysis of Optimal Goal-Oriented Adaptivity","display_name":"An Abstract Analysis of Optimal Goal-Oriented Adaptivity","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2184367770","doi":"https://doi.org/10.1137/15m1021982","mag":"2184367770"},"language":"en","primary_location":{"id":"doi:10.1137/15m1021982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1021982","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1505.04536","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Michael Feischl","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael Feischl","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Dirk Praetorius","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dirk Praetorius","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Kristoffer G. van der Zee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kristoffer G. van der Zee","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3197,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.93733342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"3","first_page":"1423","last_page":"1448"},"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":0.8615000247955322,"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":0.8615000247955322,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.02329999953508377,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.01600000075995922,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6816999912261963},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.49970000982284546},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.4966000020503998},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4683000147342682},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4657999873161316},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.40130001306533813},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3840000033378601},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.3634999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.809499979019165},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6816999912261963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5598000288009644},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.49970000982284546},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.4966000020503998},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4657999873161316},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.3634999990463257},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3452000021934509},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.3287999927997589},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.31839999556541443},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.28189998865127563},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.28130000829696655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2662999927997589},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1021982","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1021982","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:arXiv.org:1505.04536","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.04536","pdf_url":"https://arxiv.org/pdf/1505.04536","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.nottingham.ac.uk:32679","is_oa":true,"landing_page_url":"http://eprints.nottingham.ac.uk/32679/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402013","display_name":"Nottingham ePrints (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:nottingham-repository.worktribe.com:790172","is_oa":true,"landing_page_url":"https://nottingham-repository.worktribe.com/output/790172","pdf_url":null,"source":{"id":"https://openalex.org/S4306402483","display_name":"Repository@Nottingham (University of Nottingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142263535","host_organization_name":"University of Nottingham","host_organization_lineage":["https://openalex.org/I142263535"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1505.04536","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.04536","pdf_url":"https://arxiv.org/pdf/1505.04536","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1742109135","display_name":null,"funder_award_id":"W1245","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5394959934","display_name":null,"funder_award_id":"P27005","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7571794177","display_name":null,"funder_award_id":"EP/I036427/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8790285555","display_name":"SAFE Barriers - a Systems Approach For Engineered Barriers","funder_award_id":"EP/I036427/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W764222646","https://openalex.org/W1965398593","https://openalex.org/W1975804347","https://openalex.org/W1976205331","https://openalex.org/W1983072269","https://openalex.org/W1985422345","https://openalex.org/W1995242431","https://openalex.org/W1999252469","https://openalex.org/W2003277202","https://openalex.org/W2026409663","https://openalex.org/W2026655730","https://openalex.org/W2027619967","https://openalex.org/W2038115135","https://openalex.org/W2044959876","https://openalex.org/W2056470693","https://openalex.org/W2061960130","https://openalex.org/W2072811159","https://openalex.org/W2075841811","https://openalex.org/W2084743165","https://openalex.org/W2089768471","https://openalex.org/W2092037996","https://openalex.org/W2097359885","https://openalex.org/W2100726453","https://openalex.org/W2107813568","https://openalex.org/W2108534867","https://openalex.org/W2120378605","https://openalex.org/W2131660612","https://openalex.org/W2133147107","https://openalex.org/W2137664537","https://openalex.org/W2165024589"],"related_works":[],"abstract_inverted_index":{"We":[0,32],"provide":[1],"an":[2],"abstract":[3],"framework":[4,36],"for":[5,9],"optimal":[6],"goal-oriented":[7],"adaptivity":[8],"finite":[10],"element":[11,15],"methods":[12,16],"and":[13,46,55,69],"boundary":[14],"in":[17],"the":[18,81],"spirit":[19],"of":[20,40],"[C.":[21],"Carstensen":[22],"et":[23],"al.,":[24],"Comput.":[25],"Math.":[26],"Appl.,":[27],"67":[28],"(2014),":[29],"pp.":[30,64,78],"1195--1253].":[31],"prove":[33],"that":[34],"this":[35],"covers":[37],"standard":[38],"discretizations":[39],"general":[41],"second-order":[42],"linear":[43],"elliptic":[44],"PDEs":[45],"hence":[47],"generalizes":[48],"available":[49],"results":[50],"[R.":[51],"Becker,":[52],"E.":[53],"Estecahandy,":[54],"D.":[56],"Trujillo,":[57],"SIAM":[58,72],"J.":[59,73],"Numer.":[60,74],"Anal.,":[61,75],"49":[62],"(2011),":[63],"2451--2469,":[65],"M.":[66],"S.":[67],"Mommer":[68],"R.":[70],"Stevenson,":[71],"47":[76],"(2009),":[77],"861--886]":[79],"beyond":[80],"Poisson":[82],"equation.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}