{"id":"https://openalex.org/W2014670413","doi":"https://doi.org/10.1137/s1064827599356274","title":"Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries","display_name":"Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2014670413","doi":"https://doi.org/10.1137/s1064827599356274","mag":"2014670413"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827599356274","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356274","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Mark Arnold","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark Arnold","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091196582"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9375,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.75529794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"2","first_page":"673","last_page":"703"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9987999796867371,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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":0.7277699708938599},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6787398457527161},{"id":"https://openalex.org/keywords/spherical-shell","display_name":"Spherical shell","score":0.6184361577033997},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5821203589439392},{"id":"https://openalex.org/keywords/shell","display_name":"Shell (structure)","score":0.5813471674919128},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5591610074043274},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5110105276107788},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.475630521774292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45129674673080444},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4505945146083832},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4348416328430176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3348003327846527},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.0745796263217926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7277699708938599},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6787398457527161},{"id":"https://openalex.org/C108280814","wikidata":"https://www.wikidata.org/wiki/Q12137","display_name":"Spherical shell","level":3,"score":0.6184361577033997},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5821203589439392},{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.5813471674919128},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5591610074043274},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5110105276107788},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.475630521774292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45129674673080444},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4505945146083832},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4348416328430176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3348003327846527},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0745796263217926},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827599356274","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827599356274","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W138382266","https://openalex.org/W604181985","https://openalex.org/W1578723177","https://openalex.org/W1967605889","https://openalex.org/W1977464652","https://openalex.org/W1979222730","https://openalex.org/W1982691760","https://openalex.org/W1990101688","https://openalex.org/W1992011925","https://openalex.org/W2000316118","https://openalex.org/W2018648326","https://openalex.org/W2028063546","https://openalex.org/W2039726661","https://openalex.org/W2055738068","https://openalex.org/W2056658486","https://openalex.org/W2059814274","https://openalex.org/W2062335567","https://openalex.org/W2065159510","https://openalex.org/W2066779993","https://openalex.org/W2075296933","https://openalex.org/W2081330222","https://openalex.org/W2084862534","https://openalex.org/W3021722416","https://openalex.org/W3022266510","https://openalex.org/W4230941884"],"related_works":["https://openalex.org/W4389318410","https://openalex.org/W2021532954","https://openalex.org/W2006971467","https://openalex.org/W3092625298","https://openalex.org/W1984250159","https://openalex.org/W2085026264","https://openalex.org/W2031104219","https://openalex.org/W2053410843","https://openalex.org/W2389231849","https://openalex.org/W1969541928"],"abstract_inverted_index":{"A":[0],"sequence":[1],"of":[2,57],"optimal":[3],"hierarchic":[4,62,83],"models":[5,63,68,84],"is":[6,31,34,79],"derived":[7],"for":[8],"stationary":[9],"heat":[10],"conduction":[11],"on":[12,41],"the":[13,38,50,55,61,74,82,90,101],"following":[14],"laminated":[15],"domains:":[16],"a":[17,20,24,28,58],"flat":[18],"plate,":[19],"circular":[21],"arch,":[22],"and":[23,77,93],"spherical":[25,59],"shell.":[26],"An":[27],"priori":[29],"bound":[30],"presented,":[32],"which":[33,48],"evaluated":[35],"explicitly":[36],"in":[37,54,73],"homogeneous":[39],"case":[40,56],"each":[42],"domain.":[43],"Computational":[44],"examples":[45],"are":[46,64,85],"given,":[47],"illustrate":[49],"theoretical":[51],"results.":[52],"Furthermore,":[53],"shell,":[60],"compared":[65],"numerically":[66],"to":[67,100],"obtained":[69],"using":[70],"polynomial":[71,91],"approximation":[72],"radial":[75],"direction,":[76],"it":[78],"found":[80],"that":[81],"both":[86],"more":[87,95],"accurate":[88],"than":[89],"ones":[92],"provide":[94],"robust":[96],"convergence":[97],"with":[98],"respect":[99],"shell":[102],"thickness.":[103]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
