{"id":"https://openalex.org/W3125303363","doi":"https://doi.org/10.1515/jnma-2022-0038","title":"<i>A posteriori</i> error estimates for hierarchical mixed-dimensional elliptic equations","display_name":"<i>A posteriori</i> error estimates for hierarchical mixed-dimensional elliptic equations","publication_year":2022,"publication_date":"2022-10-20","ids":{"openalex":"https://openalex.org/W3125303363","doi":"https://doi.org/10.1515/jnma-2022-0038","mag":"3125303363"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2022-0038","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2022-0038","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jnma-2022-0038/pdf","source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.1515/jnma-2022-0038/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074245570","display_name":"Jhabriel Varela","orcid":"https://orcid.org/0000-0003-2220-2204"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Jhabriel Varela","raw_affiliation_strings":["University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009849700","display_name":"Elyes Ahmed","orcid":"https://orcid.org/0000-0002-6194-6356"},"institutions":[{"id":"https://openalex.org/I173888879","display_name":"SINTEF","ror":"https://ror.org/01f677e56","country_code":"NO","type":"facility","lineage":["https://openalex.org/I173888879"]},{"id":"https://openalex.org/I4387930215","display_name":"SINTEF Digital","ror":"https://ror.org/028m52w57","country_code":null,"type":"facility","lineage":["https://openalex.org/I173888879","https://openalex.org/I4387930215"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Elyes Ahmed","raw_affiliation_strings":["SINTEF Digital , Mathematics and Cybernetics , Oslo , Norway"],"affiliations":[{"raw_affiliation_string":"SINTEF Digital , Mathematics and Cybernetics , Oslo , Norway","institution_ids":["https://openalex.org/I173888879","https://openalex.org/I4387930215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016158002","display_name":"Eirik Keilegavlen","orcid":"https://orcid.org/0000-0002-0333-9507"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Eirik Keilegavlen","raw_affiliation_strings":["University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087384117","display_name":"Jan M. Nordbotten","orcid":"https://orcid.org/0000-0003-1455-5704"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Jan M. Nordbotten","raw_affiliation_strings":["University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101505057","display_name":"Florin A. Radu","orcid":"https://orcid.org/0000-0002-2577-5684"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Florin A. Radu","raw_affiliation_strings":["University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen , Center for Modeling of Coupled Subsurface Dynamics , Department of Mathematics , Bergen , Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5074245570"],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":0.9753,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67014386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"4","first_page":"247","last_page":"280"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9980999827384949,"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":0.9952999949455261,"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/discretization","display_name":"Discretization","score":0.8007837533950806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7432730197906494},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6887403726577759},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6732451915740967},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6623365879058838},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6106342077255249},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.5457183718681335},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49799323081970215},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.4445782005786896},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.42895814776420593},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.423669695854187},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3282976448535919},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.230268657207489},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18976962566375732},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.1596914827823639},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06353315711021423}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8007837533950806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7432730197906494},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6887403726577759},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6732451915740967},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6623365879058838},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6106342077255249},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.5457183718681335},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49799323081970215},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.4445782005786896},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.42895814776420593},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.423669695854187},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3282976448535919},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.230268657207489},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18976962566375732},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.1596914827823639},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06353315711021423},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/jnma-2022-0038","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2022-0038","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jnma-2022-0038/pdf","source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/jnma-2022-0038","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2022-0038","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jnma-2022-0038/pdf","source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6800000071525574,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3125303363.pdf","grobid_xml":"https://content.openalex.org/works/W3125303363.grobid-xml"},"referenced_works_count":72,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W408406386","https://openalex.org/W592911714","https://openalex.org/W614447849","https://openalex.org/W648762968","https://openalex.org/W1508861003","https://openalex.org/W1530030810","https://openalex.org/W1549748890","https://openalex.org/W1972200842","https://openalex.org/W1975208179","https://openalex.org/W1976435787","https://openalex.org/W1978286467","https://openalex.org/W1985988195","https://openalex.org/W1988871999","https://openalex.org/W1989594010","https://openalex.org/W1998397647","https://openalex.org/W2000362570","https://openalex.org/W2023515318","https://openalex.org/W2037067761","https://openalex.org/W2037836476","https://openalex.org/W2051722950","https://openalex.org/W2062618977","https://openalex.org/W2073216552","https://openalex.org/W2081180841","https://openalex.org/W2094293004","https://openalex.org/W2098763399","https://openalex.org/W2105729768","https://openalex.org/W2113227897","https://openalex.org/W2132509247","https://openalex.org/W2146683922","https://openalex.org/W2152799582","https://openalex.org/W2155395549","https://openalex.org/W2161530217","https://openalex.org/W2161741483","https://openalex.org/W2167521757","https://openalex.org/W2519971170","https://openalex.org/W2528152073","https://openalex.org/W2549516606","https://openalex.org/W2554554440","https://openalex.org/W2560651211","https://openalex.org/W2578146255","https://openalex.org/W2732088382","https://openalex.org/W2786028739","https://openalex.org/W2888666293","https://openalex.org/W2898230825","https://openalex.org/W2902196283","https://openalex.org/W2906022956","https://openalex.org/W2906573104","https://openalex.org/W2908252308","https://openalex.org/W2914124241","https://openalex.org/W2914755363","https://openalex.org/W2949694278","https://openalex.org/W2954169627","https://openalex.org/W2959722367","https://openalex.org/W2962837672","https://openalex.org/W2962856640","https://openalex.org/W2963719190","https://openalex.org/W3000417331","https://openalex.org/W3002284018","https://openalex.org/W3005601165","https://openalex.org/W3036962076","https://openalex.org/W3080416157","https://openalex.org/W3080670400","https://openalex.org/W3092750238","https://openalex.org/W3096481337","https://openalex.org/W3139180147","https://openalex.org/W4211097011","https://openalex.org/W4236225822","https://openalex.org/W4256522009","https://openalex.org/W4285719527","https://openalex.org/W4292993127","https://openalex.org/W6601654347"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W1971388572","https://openalex.org/W2370926798","https://openalex.org/W2793786119","https://openalex.org/W4234142113","https://openalex.org/W3145389907"],"abstract_inverted_index":{"Abstract":[0],"Mixed-dimensional":[1],"elliptic":[2],"equations":[3],"exhibiting":[4],"a":[5,37,127,135],"hierarchical":[6],"structure":[7,129],"are":[8,59],"commonly":[9],"used":[10],"to":[11,130],"model":[12],"problems":[13,157],"with":[14,68,126],"high":[15],"aspect":[16],"ratio":[17],"inclusions,":[18],"such":[19],"as":[20],"flow":[21,164],"in":[22,109,165],"fractured":[23,166],"porous":[24,167],"media.":[25,168],"We":[26,61,138],"derive":[27],"general":[28],"abstract":[29,65],"estimates":[30,114],"based":[31,82,160],"on":[32,63,83,161],"the":[33,47,56,64,69,79,84,86,121,140],"theory":[34],"of":[35,77,143,163],"functional":[36,70],"posteriori":[38,136],"error":[39],"estimates,":[40],"for":[41,46,55,155],"which":[42],"guaranteed":[43],"upper":[44],"bounds":[45,54],"primal":[48],"and":[49,52,102,111,158],"dual":[50],"variables":[51],"two-sided":[53],"primal\u2013dual":[57],"pair":[58],"obtained.":[60],"improve":[62],"results":[66,108,146],"obtained":[67,132],"approach":[71],"by":[72],"proposing":[73],"four":[74,151],"different":[75,152],"ways":[76],"estimating":[78],"residual":[80],"errors":[81],"extent":[85],"approximate":[87],"solution":[88],"has":[89],"conservation":[90],"properties,":[91],"i.e.,":[92],"(1)":[93],"no":[94],"conservation,":[95,98,101],"(2)":[96],"subdomain":[97],"(3)":[99],"grid-level":[100],"(4)":[103],"exact":[104],"conservation.":[105],"This":[106],"treatment":[107],"sharper":[110],"fully":[112],"computable":[113],"when":[115],"mass":[116],"is":[117],"conserved":[118],"either":[119],"at":[120],"grid":[122],"level":[123],"or":[124],"exactly,":[125],"comparable":[128],"those":[131],"from":[133],"grid-based":[134],"techniques.":[137],"demonstrate":[139],"practical":[141],"effectiveness":[142],"our":[144],"theoretical":[145],"through":[147],"numerical":[148],"experiments":[149],"using":[150],"discretization":[153],"methods":[154],"synthetic":[156],"applications":[159],"benchmarks":[162]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
