{"id":"https://openalex.org/W2006810111","doi":"https://doi.org/10.1137/s0036142900370125","title":"Least-Squares Galerkin Methods for Parabolic Problems I: Semidiscretization in Time","display_name":"Least-Squares Galerkin Methods for Parabolic Problems I: Semidiscretization in Time","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2006810111","doi":"https://doi.org/10.1137/s0036142900370125","mag":"2006810111"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900370125","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900370125","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":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066679330","display_name":"Gerhard Starke","orcid":"https://orcid.org/0000-0001-5985-173X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerhard Starke","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051984513"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0605,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76344674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"39","issue":"4","first_page":"1302","last_page":"1323"},"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":0.9993000030517578,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9980999827384949,"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":0.883309006690979},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6441454887390137},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6186989545822144},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5826740264892578},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5737625956535339},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5091764330863953},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4980192184448242},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4933113157749176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46528688073158264},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4578998386859894},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4282238483428955},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.42550987005233765},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4151473045349121},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.25817567110061646},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.11078548431396484},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09290874004364014},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07947343587875366}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.883309006690979},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6441454887390137},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6186989545822144},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5826740264892578},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5737625956535339},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5091764330863953},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4980192184448242},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4933113157749176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46528688073158264},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4578998386859894},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4282238483428955},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.42550987005233765},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4151473045349121},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25817567110061646},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.11078548431396484},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09290874004364014},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07947343587875366},{"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/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":2,"locations":[{"id":"doi:10.1137/s0036142900370125","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900370125","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:10.1.1.42.8341","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.8341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uni-essen.de/~matp00/pub/timelsqr.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W62043397","https://openalex.org/W1972792313","https://openalex.org/W1973085268","https://openalex.org/W1988975817","https://openalex.org/W1992363799","https://openalex.org/W2034298604","https://openalex.org/W2038626747","https://openalex.org/W2064416388","https://openalex.org/W2082621526","https://openalex.org/W2085401519","https://openalex.org/W2132292023","https://openalex.org/W3021722416","https://openalex.org/W4242273588"],"related_works":["https://openalex.org/W2982093746","https://openalex.org/W3043435143","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W1995357705","https://openalex.org/W2490196280","https://openalex.org/W3208509670"],"abstract_inverted_index":{"This":[0,45,86],"is":[1,76,87,150],"the":[2,24,48,68,73,77,83,91,94,98,111,121,137,144,153,157],"first":[3],"part":[4],"of":[5,8,26,52,67,72,90,93,124],"a":[6,27,79,88,103,147],"series":[7],"papers":[9],"on":[10,23,120],"least-squares":[11,28,60,74,95],"Galerkin":[12],"methods":[13,20,54],"for":[14,30,55,62,82,136,152],"parabolic":[15,64],"initial-boundary":[16],"value":[17],"problems.":[18,65],"These":[19],"are":[21],"based":[22],"minimization":[25],"functional":[29,96],"an":[31,107],"equivalent":[32],"first-order":[33],"system":[34],"over":[35],"space":[36],"and":[37,50,139,156],"time":[38,58],"with":[39,102,131],"respect":[40],"to":[41,97],"suitable":[42],"discrete":[43],"spaces.":[44],"paper":[46],"presents":[47],"derivation":[49],"analysis":[51],"one-step":[53],"semi-discretization":[56],"in":[57,106,113],"from":[59],"principles":[61],"linear":[63,134],"One":[66],"most":[69],"important":[70],"features":[71],"methodology":[75],"built-in":[78],"posteriori":[80],"estimate":[81],"approximation":[84],"error.":[85],"consequence":[89],"equivalence":[92],"consistency":[99],"error":[100],"associated":[101,158],"time-step,":[104],"measured":[105],"appropriate":[108],"norm.":[109],"For":[110,143],"presentation":[112],"this":[114],"paper,":[115],"we":[116],"focus":[117],"our":[118],"attention":[119],"specific":[122],"combination":[123],"piecewise":[125,133],"linear,":[126],"not":[127],"necessarily":[128],"continuous,":[129],"functions":[130,135],"continuous":[132],"flux":[138],"scalar":[140,154],"variable,":[141],"respectively.":[142],"resulting":[145],"method,":[146],"convergence":[148],"result":[149],"shown":[151],"variable":[155],"flux.":[159]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
