{"id":"https://openalex.org/W2062557957","doi":"https://doi.org/10.1137/s0036142902413615","title":"Estimation of Higher Sobolev Norm from Lower Order Approximation","display_name":"Estimation of Higher Sobolev Norm from Lower Order Approximation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2062557957","doi":"https://doi.org/10.1137/s0036142902413615","mag":"2062557957"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902413615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902413615","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/A5036808184","display_name":"Carsten Carstensen","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Carsten Carstensen","raw_affiliation_strings":["Humboldt\u2010University of Berlin\u2028"],"affiliations":[{"raw_affiliation_string":"Humboldt\u2010University of Berlin\u2028","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036808184"],"corresponding_institution_ids":["https://openalex.org/I39343248"],"apc_list":null,"apc_paid":null,"fwci":0.8251,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.73940224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"42","issue":"5","first_page":"2136","last_page":"2147"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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":0.8841904401779175},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7385222911834717},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.683334231376648},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6634462475776672},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6211792230606079},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6115145087242126},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5748651623725891},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4680939018726349},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.44358089566230774},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4415535628795624},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43002837896347046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37722674012184143},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.373775839805603},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08790937066078186},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07712066173553467}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8841904401779175},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7385222911834717},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.683334231376648},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6634462475776672},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6211792230606079},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6115145087242126},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5748651623725891},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4680939018726349},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.44358089566230774},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4415535628795624},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43002837896347046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37722674012184143},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.373775839805603},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08790937066078186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07712066173553467},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142902413615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902413615","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W744342512","https://openalex.org/W1533889494","https://openalex.org/W1995404822","https://openalex.org/W2071036364","https://openalex.org/W2074772185","https://openalex.org/W2079232547","https://openalex.org/W2092047978","https://openalex.org/W2106327313","https://openalex.org/W2133147107","https://openalex.org/W2146115533","https://openalex.org/W2157121531","https://openalex.org/W2505585705"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W4292947165","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W789026155","https://openalex.org/W3042022377"],"abstract_inverted_index":{"Given":[0],"an":[1,55,69],"accurate":[2],"piecewise":[3],"constant":[4],"flux":[5,14],"approximation":[6,56],"q":[7],"of":[8,23,37,58,74],"a":[9,20,26,34,41],"smooth":[10],"(but":[11],"unknown)":[12],"exact":[13],"p,":[15],"how":[16],"can":[17],"one":[18],"compute":[19],"Sobolev":[21],"norm":[22],"p":[24],"over":[25],"small":[27],"domain":[28],"$\\omega$?":[29],"This":[30],"question":[31],"arises":[32],"in":[33],"duality":[35],"argument":[36],"goal-oriented":[38],"finite":[39],"element":[40],"posteriori":[42],"error":[43],"analysis.":[44],"Two":[45],"equivalent":[46],"practical":[47],"estimators":[48],"$\\eta_{M}$":[49],"and":[50,60,71],"$\\eta_{\\mathcal{E}}$":[51],"are":[52,63],"presented":[53],"for":[54],"$\\!q\\!$":[57,66],"$|p|_{H^1(\\omega)}$":[59],"model":[61],"situations":[62],"addressed":[64],"where":[65],"is":[67],"asymptotically":[68],"upper":[70],"+lower":[72],"bound":[73],"$|p|_{H^1(\\Omega)}$.":[75]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}