{"id":"https://openalex.org/W2016230194","doi":"https://doi.org/10.1137/s0036142902409185","title":"Least-Squares Galerkin Methods for Parabolic Problems III: Semidiscrete Case for Semilinear Problems","display_name":"Least-Squares Galerkin Methods for Parabolic Problems III: Semidiscrete Case for Semilinear Problems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2016230194","doi":"https://doi.org/10.1137/s0036142902409185","mag":"2016230194"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902409185","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902409185","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/A5051984513","display_name":"Mohammad Majidi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mohammad Majidi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051984513"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13370697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"6","first_page":"2452","last_page":"2475"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9987999796867371,"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":0.9979000091552734,"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":0.8993561863899231},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6897925138473511},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5779892802238464},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5691367387771606},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5562520027160645},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5234317779541016},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5048866868019104},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47745612263679504},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4695746600627899},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4535667300224304},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3349366784095764},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07302731275558472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8993561863899231},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6897925138473511},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5779892802238464},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5691367387771606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5562520027160645},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5234317779541016},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5048866868019104},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47745612263679504},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4695746600627899},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4535667300224304},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3349366784095764},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07302731275558472},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/s0036142902409185","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902409185","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":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W62043397","https://openalex.org/W1518527542","https://openalex.org/W1527296550","https://openalex.org/W1560060148","https://openalex.org/W1575147392","https://openalex.org/W1970850839","https://openalex.org/W1972792313","https://openalex.org/W1973085268","https://openalex.org/W1976338762","https://openalex.org/W1988975817","https://openalex.org/W2005722356","https://openalex.org/W2006810111","https://openalex.org/W2034298604","https://openalex.org/W2038626747","https://openalex.org/W2043971663","https://openalex.org/W2064416388","https://openalex.org/W2070986612","https://openalex.org/W2082621526","https://openalex.org/W2084005055","https://openalex.org/W2085401519","https://openalex.org/W2304392699","https://openalex.org/W2429258439","https://openalex.org/W3021722416","https://openalex.org/W4231463495","https://openalex.org/W4240361988","https://openalex.org/W4242273588","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1967648380","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2109304297","https://openalex.org/W2100864966","https://openalex.org/W2083709218"],"abstract_inverted_index":{"This":[0,45],"is":[1,76,127],"the":[2,24,48,68,73,83,87,97,114,121,130],"third":[3],"part":[4],"of":[5,8,26,52,67,72,100],"a":[6,27,77,79,124],"series":[7],"papers":[9],"on":[10,23,96],"least-squares":[11,28,60,74],"Galerkin":[12],"methods":[13,20,54],"for":[14,30,55,62,82,113,129],"parabolic":[15,64],"initial-boundary":[16],"value":[17],"problems.":[18,65],"These":[19],"are":[21],"based":[22],"minimization":[25],"functional":[29],"an":[31],"equivalent":[32],"first-order":[33],"system":[34],"over":[35],"space":[36],"and":[37,50,116],"time":[38,58,108],"with":[39,109],"respect":[40],"to":[41],"suitable":[42],"discrete":[43],"spaces.":[44],"paper":[46],"presents":[47],"derivation":[49],"analysis":[51],"one-step":[53],"semidiscretization":[56],"in":[57,89,107],"from":[59],"principles":[61],"semilinear":[63],"One":[66],"most":[69],"important":[70],"features":[71],"methodology":[75],"built-in":[78],"posteriori":[80],"estimate":[81],"approximation":[84],"error.":[85],"For":[86,120],"presentation":[88],"this":[90],"paper,":[91],"we":[92],"focus":[93],"our":[94],"attention":[95],"specific":[98],"combination":[99],"piecewise":[101,111],"linear,":[102],"not":[103],"necessarily":[104],"continuous,":[105],"functions":[106],"continuous":[110],"linear":[112],"flux":[115],"scalar":[117,131],"variables,":[118],"respectively.":[119],"resulting":[122],"method,":[123],"convergence":[125],"result":[126],"shown":[128],"variable.":[132]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
