{"id":"https://openalex.org/W2002848627","doi":"https://doi.org/10.1137/s0036142900379679","title":"Galerkin Methods in Age and Space for a Population Model with Nonlinear Diffusion","display_name":"Galerkin Methods in Age and Space for a Population Model with Nonlinear Diffusion","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2002848627","doi":"https://doi.org/10.1137/s0036142900379679","mag":"2002848627"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900379679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900379679","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/A5058526947","display_name":"Bruce P. Ayati","orcid":"https://orcid.org/0000-0002-4472-6271"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bruce P. Ayati","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102273369","display_name":"Todd F. Dupont","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Todd F. Dupont","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058526947"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6772,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.75623308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"3","first_page":"1064","last_page":"1076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.8560497760772705},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.8060662150382996},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6185678243637085},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5953962802886963},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.5454677939414978},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5449842214584351},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5367359519004822},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5069175362586975},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.503940761089325},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4742759168148041},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46936991810798645},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.46766698360443115},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45854973793029785},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45326563715934753},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4378662407398224},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.41865861415863037},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.158900648355484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1274918019771576}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8560497760772705},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.8060662150382996},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6185678243637085},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5953962802886963},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.5454677939414978},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5449842214584351},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5367359519004822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5069175362586975},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.503940761089325},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4742759168148041},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46936991810798645},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.46766698360443115},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45854973793029785},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45326563715934753},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4378662407398224},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.41865861415863037},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.158900648355484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1274918019771576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142900379679","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900379679","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.53.4928","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.4928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uchicago.edu/publications/tech-reports/TR-98-10.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W193216737","https://openalex.org/W1788856903","https://openalex.org/W1893052487","https://openalex.org/W1965584544","https://openalex.org/W1976117045","https://openalex.org/W1982306633","https://openalex.org/W1982540504","https://openalex.org/W1998371313","https://openalex.org/W2018874086","https://openalex.org/W2024277916","https://openalex.org/W2047378168","https://openalex.org/W2065601190","https://openalex.org/W2121953505","https://openalex.org/W2151807147","https://openalex.org/W2554680890"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W2891538916","https://openalex.org/W1565666028","https://openalex.org/W4230524683","https://openalex.org/W2160252404","https://openalex.org/W4318305492","https://openalex.org/W2508014856","https://openalex.org/W2055696851","https://openalex.org/W2036064357"],"abstract_inverted_index":{"We":[0],"present":[1],"Galerkin":[2],"methods":[3,19,80],"in":[4,30,57,60,86],"both":[5],"the":[6,27,33,44,54,61,67,87],"age":[7,31,88],"and":[8],"space":[9,29,34,56],"variables":[10],"for":[11],"an":[12],"age-dependent":[13],"population":[14],"undergoing":[15],"nonlinear":[16],"diffusion.":[17],"The":[18,72,79],"presented":[20],"are":[21,81],"a":[22],"generalization":[23],"of":[24,35,46,51],"methods,":[25],"where":[26],"approximation":[28,55],"is":[32],"piecewise":[36,48,62],"constant":[37,63],"functions.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42,65],"allow":[43],"use":[45],"discontinuous":[47],"polynomial":[49],"subspaces":[50],"L2":[52],"as":[53],"age.":[58],"As":[59],"case,":[64],"move":[66],"discretization":[68],"along":[69],"characteristic":[70],"lines.":[71],"time":[73],"variable":[74],"has":[75],"been":[76],"left":[77],"continuous.":[78],"shown":[82],"to":[83],"be":[84],"superconvergent":[85],"variable.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}