{"id":"https://openalex.org/W2784974683","doi":"https://doi.org/10.1137/16m1106626","title":"A Petrov--Galerkin Kernel Approximation on the Sphere","display_name":"A Petrov--Galerkin Kernel Approximation on the Sphere","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2784974683","doi":"https://doi.org/10.1137/16m1106626","mag":"2784974683"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106626","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/A5061434040","display_name":"Davoud Mirzaei","orcid":"https://orcid.org/0000-0002-0166-4760"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Davoud Mirzaei","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061434040"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3598,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76458117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"56","issue":"1","first_page":"274","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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":0.9991999864578247,"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":0.9983999729156494,"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/mathematics","display_name":"Mathematics","score":0.8824712038040161},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.7916131615638733},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7628523707389832},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6528280377388},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5852220058441162},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.577420175075531},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5446996688842773},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.5193861126899719},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47428709268569946},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43303531408309937},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21941933035850525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06489890813827515}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8824712038040161},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.7916131615638733},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7628523707389832},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6528280377388},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5852220058441162},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.577420175075531},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5446996688842773},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.5193861126899719},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47428709268569946},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43303531408309937},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21941933035850525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06489890813827515},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1106626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106626","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":[{"id":"https://openalex.org/G4027181296","display_name":null,"funder_award_id":"95650077","funder_id":"https://openalex.org/F4320323645","funder_display_name":"Institute for Research in Fundamental Sciences"}],"funders":[{"id":"https://openalex.org/F4320323645","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W120550985","https://openalex.org/W123519660","https://openalex.org/W1486164486","https://openalex.org/W1491507172","https://openalex.org/W1578723177","https://openalex.org/W1963785789","https://openalex.org/W1973878509","https://openalex.org/W1988604300","https://openalex.org/W1988793248","https://openalex.org/W1991137104","https://openalex.org/W1995274909","https://openalex.org/W1996710757","https://openalex.org/W2003971308","https://openalex.org/W2016969219","https://openalex.org/W2017142556","https://openalex.org/W2023638740","https://openalex.org/W2032523091","https://openalex.org/W2036326859","https://openalex.org/W2040314635","https://openalex.org/W2069887143","https://openalex.org/W2076577157","https://openalex.org/W2084196626","https://openalex.org/W2102596289","https://openalex.org/W2109565734","https://openalex.org/W2127689830","https://openalex.org/W2155307607","https://openalex.org/W2160615084","https://openalex.org/W2161591817","https://openalex.org/W2964094877","https://openalex.org/W3099812454"],"related_works":["https://openalex.org/W2502192667","https://openalex.org/W4386492213","https://openalex.org/W4288262055","https://openalex.org/W2967076701","https://openalex.org/W2990320605","https://openalex.org/W1982675504","https://openalex.org/W2144405044","https://openalex.org/W4321472236","https://openalex.org/W4389325935","https://openalex.org/W2167486107"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,18,25],"numerical":[4,73,92],"solution":[5,74],"of":[6,32,52,60,79],"partial":[7],"differential":[8],"equations":[9],"on":[10],"the":[11,33,38,53,69,72,84],"unit":[12],"sphere":[13],"is":[14,35,56,65,105],"given":[15],"by":[16],"using":[17],"kernel":[19],"trial":[20,70],"approximation":[21,109],"in":[22,45,58,68,77,83],"combination":[23],"with":[24],"special":[26],"Petrov--Galerkin":[27],"test":[28,85],"discretization.":[29],"The":[30,49,63],"solvability":[31],"scheme":[34],"proved,":[36],"and":[37,82],"error":[39],"bounds":[40],"are":[41],"obtained":[42],"for":[43,107],"functions":[44],"appropriate":[46],"Sobolev":[47],"spaces.":[48],"condition":[50],"number":[51],"final":[54],"system":[55],"estimated":[57],"terms":[59,78],"discretization":[61],"parameters.":[62],"method":[64],"meshless":[66],"because":[67],"side":[71,86],"parameterizes":[75],"entirely":[76],"scattered":[80],"points":[81],"everything":[87],"breaks":[88],"down":[89],"to":[90],"simple":[91],"integrations":[93],"over":[94],"independent":[95],"spherical":[96],"caps.":[97],"This":[98],"means":[99],"that":[100],"no":[101],"connected":[102],"background":[103],"mesh":[104],"required":[106],"either":[108],"or":[110],"integration.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}