{"id":"https://openalex.org/W3118385539","doi":"https://doi.org/10.1007/s10915-021-01417-y","title":"Reliable Residual-Based Error Estimation for the Finite Cell Method","display_name":"Reliable Residual-Based Error Estimation for the Finite Cell Method","publication_year":2021,"publication_date":"2021-02-23","ids":{"openalex":"https://openalex.org/W3118385539","doi":"https://doi.org/10.1007/s10915-021-01417-y","mag":"3118385539"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01417-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01417-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01417-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01417-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037722544","display_name":"Paolo Di Stolfo","orcid":"https://orcid.org/0000-0001-5735-5644"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Paolo Di Stolfo","raw_affiliation_strings":["University of Salzburg, Hellbrunner Stra\u00dfe 34, 5020, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"University of Salzburg, Hellbrunner Stra\u00dfe 34, 5020, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021218669","display_name":"J\u00f6rg Schr\u00f6der","orcid":"https://orcid.org/0000-0003-3691-0906"},"institutions":[{"id":"https://openalex.org/I182212641","display_name":"University of Salzburg","ror":"https://ror.org/05gs8cd61","country_code":"AT","type":"education","lineage":["https://openalex.org/I182212641"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Andreas Schr\u00f6der","raw_affiliation_strings":["University of Salzburg, Hellbrunner Stra\u00dfe 34, 5020, Salzburg, Austria"],"affiliations":[{"raw_affiliation_string":"University of Salzburg, Hellbrunner Stra\u00dfe 34, 5020, Salzburg, Austria","institution_ids":["https://openalex.org/I182212641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037722544"],"corresponding_institution_ids":["https://openalex.org/I182212641"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.1751,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41128051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"87","issue":"1","first_page":null,"last_page":null},"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/T10514","display_name":"Numerical methods in engineering","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/estimator","display_name":"Estimator","score":0.9044573307037354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7773531675338745},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.7323368787765503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.583483099937439},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5320592522621155},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.48239147663116455},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4714943766593933},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.45411160588264465},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4198361039161682},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4108864665031433},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3847680985927582},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.3421086370944977},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2610059380531311},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22086897492408752},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16758471727371216}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.9044573307037354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7773531675338745},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.7323368787765503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.583483099937439},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5320592522621155},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.48239147663116455},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4714943766593933},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.45411160588264465},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4198361039161682},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4108864665031433},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3847680985927582},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3421086370944977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2610059380531311},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22086897492408752},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16758471727371216},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-021-01417-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01417-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01417-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01417-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01417-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01417-y.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8650729352","display_name":null,"funder_award_id":"SCHR 1244/4-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323345","display_name":"Universit\u00e4t Salzburg","ror":"https://ror.org/05gs8cd61"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3118385539.pdf","grobid_xml":"https://content.openalex.org/works/W3118385539.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W94458352","https://openalex.org/W768066628","https://openalex.org/W1479835491","https://openalex.org/W1488877410","https://openalex.org/W1572985915","https://openalex.org/W1964155345","https://openalex.org/W1968144724","https://openalex.org/W1992833209","https://openalex.org/W2008065952","https://openalex.org/W2022158978","https://openalex.org/W2026812854","https://openalex.org/W2030028670","https://openalex.org/W2064700919","https://openalex.org/W2066254214","https://openalex.org/W2078092264","https://openalex.org/W2080811944","https://openalex.org/W2086543645","https://openalex.org/W2091662710","https://openalex.org/W2093376848","https://openalex.org/W2094548551","https://openalex.org/W2096029655","https://openalex.org/W2106079716","https://openalex.org/W2171898633","https://openalex.org/W2298109381","https://openalex.org/W2342243630","https://openalex.org/W2600485508","https://openalex.org/W2739323679","https://openalex.org/W2751842246","https://openalex.org/W2791787432","https://openalex.org/W2795864004","https://openalex.org/W2947118943","https://openalex.org/W2966452845","https://openalex.org/W2969522957","https://openalex.org/W2980098156","https://openalex.org/W2987883181","https://openalex.org/W2996414013","https://openalex.org/W4229598638","https://openalex.org/W4232433165","https://openalex.org/W6601616708"],"related_works":["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/W2954004777","https://openalex.org/W2362625355","https://openalex.org/W2566764723","https://openalex.org/W1572069104"],"abstract_inverted_index":{"Abstract":[0],"In":[1,167],"this":[2],"work,":[3],"the":[4,12,24,44,64,69,75,87,100,103,112,122,140,156,168,170,173,196,203],"reliability":[5,41,171],"of":[6,26,43,51,86,102,111,121,158,172,202],"a":[7,53,94,159,210,214],"residual-based":[8,52],"error":[9,19,45,55,65,123,174,197,204],"estimator":[10,20,46,124,175,205],"for":[11,23,33,178,187,209],"Finite":[13],"Cell":[14],"method":[15],"is":[16,21,125,176,206],"established.":[17],"The":[18,40,119,199],"suitable":[22],"application":[25],"hp":[27,188],"-adaptive":[28,192],"finite":[29],"elements":[30],"and":[31,80,93,116,181,190],"allows":[32],"Neumann":[34,81],"boundary":[35,82,107],"conditions":[36],"on":[37,48,105,139,147,162],"curved":[38],"boundaries.":[39],"proof":[42,88],"relies":[47],"standard":[49],"arguments":[50],"posteriori":[54],"control,":[56],"but":[57],"includes":[58],"several":[59],"modifications":[60],"with":[61,68,155,213],"respect":[62],"to":[63],"contributions":[66],"associated":[67],"volume":[70],"residuals":[71],"as":[72,74,184,186],"well":[73,185],"jumps":[76],"across":[77],"inner":[78],"edges":[79],"parts.":[83],"Important":[84],"ingredients":[85],"are":[89],"Stein\u2019s":[90],"extension":[91],"theorem":[92,97],"modified":[95],"trace":[96,104],"which":[98,133],"estimates":[99],"norm":[101],"(curved)":[106],"parts":[108],"in":[109],"terms":[110],"local":[113],"mesh":[114],"size":[115],"polynomial":[117],"degree.":[118],"efficiency":[120,136,154],"also":[126,207],"considered":[127],"by":[128,195],"discussing":[129],"an":[130,135],"artificial":[131],"example":[132],"yields":[134],"index":[137],"depending":[138],"mesh-family":[141],"parameter":[142],"h":[143,179,191],".":[144],"Numerical":[145],"experiments":[146,169],"more":[148],"realistic":[149],"domains,":[150],"however,":[151],"suggest":[152],"global":[153],"occurrence":[157],"large":[160],"overestimation":[161],"only":[163],"few":[164],"cut":[165],"elements.":[166],"demonstrated":[177],"-":[180],"p":[182],"-uniform":[183],"-geometric":[189],"refinements":[193],"driven":[194],"estimator.":[198],"practical":[200],"applicability":[201],"studied":[208],"3D":[211],"problem":[212],"non-smooth":[215],"solution.":[216]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}