{"id":"https://openalex.org/W2041341533","doi":"https://doi.org/10.1137/050636504","title":"The $L^2$ Norm Error Estimates for the Div Least\u2010Squares Method","display_name":"The $L^2$ Norm Error Estimates for the Div Least\u2010Squares Method","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2041341533","doi":"https://doi.org/10.1137/050636504","mag":"2041341533"},"language":"en","primary_location":{"id":"doi:10.1137/050636504","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050636504","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/A5023481731","display_name":"Zhiqiang Cai","orcid":"https://orcid.org/0000-0002-3775-7248"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhiqiang Cai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109249387","display_name":"JaEun Ku","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jaeun Ku","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023481731"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6455,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.82825311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"4","first_page":"1721","last_page":"1734"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8719345331192017},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.710708498954773},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5211503505706787},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5209513902664185},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49761083722114563},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.44711464643478394},{"id":"https://openalex.org/keywords/total-least-squares","display_name":"Total least squares","score":0.42779144644737244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3750477433204651},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2828190326690674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16688135266304016},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.12714755535125732}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8719345331192017},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.710708498954773},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5211503505706787},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5209513902664185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49761083722114563},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.44711464643478394},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.42779144644737244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3750477433204651},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2828190326690674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16688135266304016},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.12714755535125732},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050636504","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050636504","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":20,"referenced_works":["https://openalex.org/W33781092","https://openalex.org/W136185420","https://openalex.org/W1965034652","https://openalex.org/W1976140148","https://openalex.org/W1985506636","https://openalex.org/W2008004031","https://openalex.org/W2021126092","https://openalex.org/W2030826026","https://openalex.org/W2034081303","https://openalex.org/W2041056535","https://openalex.org/W2041523977","https://openalex.org/W2051682834","https://openalex.org/W2054379037","https://openalex.org/W2055026486","https://openalex.org/W2070727579","https://openalex.org/W2071942565","https://openalex.org/W2078369659","https://openalex.org/W2086713976","https://openalex.org/W2093564081","https://openalex.org/W2132292023"],"related_works":["https://openalex.org/W1986698577","https://openalex.org/W2034819163","https://openalex.org/W2352570898","https://openalex.org/W2125225254","https://openalex.org/W2043225268","https://openalex.org/W4380487384","https://openalex.org/W2374560502","https://openalex.org/W2368940260","https://openalex.org/W1997267293","https://openalex.org/W2393100698"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"$L^2$":[3,70],"norm":[4,25,60,71],"error":[5,54,72],"estimates":[6,55,73],"for":[7,12,26,37,74],"the":[8,14,22,27,38,44,57,75,79],"div":[9],"least\u2010squares":[10,17],"method":[11],"which":[13],"associated":[15],"homogeneous":[16],"functional":[18],"is":[19],"equivalent":[20],"to":[21],"$H(\\mbox{div})\\times":[23,58],"H^1$":[24,59],"respective":[28],"dual":[29],"and":[30,43,53],"primal":[31,76],"variables.":[32],"Least\u2010squares":[33],"of":[34,51],"this":[35,65],"type":[36],"second\u2010order":[39],"elliptic":[40],"equations,":[41],"elasticity,":[42],"Stokes":[45],"equations":[46],"are":[47],"an":[48],"active":[49],"area":[50],"research,":[52],"in":[56],"were":[61],"previously":[62],"established.":[63],"In":[64],"paper,":[66],"we":[67],"establish":[68],"optimal":[69],"variable":[77],"under":[78],"minimum":[80],"regularity":[81],"requirement":[82],"through":[83],"a":[84],"refined":[85],"duality":[86],"argument.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}