{"id":"https://openalex.org/W2045981428","doi":"https://doi.org/10.1515/cmam-2014-0002","title":"Goal-Oriented Error Estimation for the Fractional Step Theta Scheme","display_name":"Goal-Oriented Error Estimation for the Fractional Step Theta Scheme","publication_year":2014,"publication_date":"2014-01-16","ids":{"openalex":"https://openalex.org/W2045981428","doi":"https://doi.org/10.1515/cmam-2014-0002","mag":"2045981428"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2014-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2014-0002","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/A5083733943","display_name":"Dominik Meidner","orcid":"https://orcid.org/0000-0002-4949-6356"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dominik Meidner","raw_affiliation_strings":["Chair of Optimal Control, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstr. 3, 85748 Garching, Germany","Technical University of Munich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Optimal Control, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstr. 3, 85748 Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technical University of Munich","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060011936","display_name":"Thomas Richter","orcid":"https://orcid.org/0000-0003-0206-3606"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Richter","raw_affiliation_strings":["Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083733943"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":2.4951,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.8798907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"203","last_page":"230"},"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":0.9998999834060669,"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"}},"topics":[{"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":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.772602915763855},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6758707761764526},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6605992913246155},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5844761729240417},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.5816590785980225},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.5193125605583191},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5024795532226562},{"id":"https://openalex.org/keywords/method-of-mean-weighted-residuals","display_name":"Method of mean weighted residuals","score":0.49852561950683594},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.44971829652786255},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4409894645214081},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3708217442035675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31966349482536316},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2142537534236908}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.772602915763855},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6758707761764526},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6605992913246155},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5844761729240417},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.5816590785980225},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.5193125605583191},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5024795532226562},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.49852561950683594},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.44971829652786255},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4409894645214081},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3708217442035675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31966349482536316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2142537534236908},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1515/cmam-2014-0002","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2014-0002","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.715.3889","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.715.3889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www-m17.ma.tum.de/foswiki/pub/M17/Lehrstuhl/Public/meidner_richter_2014_I.pdf","raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1658921","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1658921","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1966619711","https://openalex.org/W1970850839","https://openalex.org/W1995404822","https://openalex.org/W1998967184","https://openalex.org/W2005152402","https://openalex.org/W2012560715","https://openalex.org/W2015788535","https://openalex.org/W2022936648","https://openalex.org/W2025163266","https://openalex.org/W2028138779","https://openalex.org/W2038626747","https://openalex.org/W2041523977","https://openalex.org/W2043267610","https://openalex.org/W2043841940","https://openalex.org/W2051862019","https://openalex.org/W2055360045","https://openalex.org/W2060546108","https://openalex.org/W2065106256","https://openalex.org/W2067218091","https://openalex.org/W2071036364","https://openalex.org/W2073256259","https://openalex.org/W2082621526","https://openalex.org/W2091336985","https://openalex.org/W2119647616","https://openalex.org/W2133147107","https://openalex.org/W2148639620","https://openalex.org/W2410260937","https://openalex.org/W2429258439","https://openalex.org/W2494971360","https://openalex.org/W2531536144","https://openalex.org/W2934526567"],"related_works":["https://openalex.org/W4238745867","https://openalex.org/W2027900078","https://openalex.org/W1927950711","https://openalex.org/W1577720732","https://openalex.org/W2790191500","https://openalex.org/W245731268","https://openalex.org/W2121515439","https://openalex.org/W2071875410","https://openalex.org/W4229335327","https://openalex.org/W209073009"],"abstract_inverted_index":{"Abstract.":[0],"In":[1],"this":[2],"work,":[3],"we":[4],"derive":[5],"a":[6,8,98,105],"goal-oriented":[7],"posteriori":[9],"error":[10,14,93,108,116,139],"estimator":[11,94,117],"for":[12],"the":[13,25,39,56,65,69,111,127,137],"due":[15],"to":[16,104,110],"time-discretization":[17],"of":[18,38,64],"nonlinear":[19],"parabolic":[20],"partial":[21],"differential":[22],"equations":[23],"by":[24,35,60,126],"fractional":[26,70],"step":[27,71],"theta":[28,41,66,72,112],"method.":[29,58],"This":[30],"time-stepping":[31,67,73,113,141],"scheme":[32,74,142],"is":[33,75,87,95,102,118],"assembled":[34,119],"three":[36,62],"steps":[37],"general":[40],"method,":[42],"that":[43,101],"also":[44],"unifies":[45],"simple":[46],"schemes":[47],"like":[48],"forward":[49],"and":[50,82,86,132,143],"backward":[51],"Euler":[52],"as":[53,55,120],"well":[54],"Crank\u2013Nicolson":[57],"Further,":[59],"combining":[61],"substeps":[63],"scheme,":[68],"derived.":[76],"It":[77],"possesses":[78],"highly":[79],"desired":[80],"stability":[81],"numerical":[83,106],"dissipation":[84],"properties":[85],"second":[88],"order":[89],"accurate.":[90],"The":[91,115],"derived":[92],"based":[96],"on":[97],"Petrov\u2013Galerkin":[99,144],"formulation":[100],"up":[103],"quadrature":[107],"equivalent":[109],"scheme.":[114],"one":[121,133],"weighted":[122,129],"residual":[123,130,135],"term":[124],"given":[125],"dual":[128],"method":[131],"additional":[134],"estimating":[136],"Galerkin":[138],"between":[140],"formulation.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
