{"id":"https://openalex.org/W2156538787","doi":"https://doi.org/10.1137/s0036142998335893","title":"Postprocessing the Galerkin Method: The Finite-Element Case","display_name":"Postprocessing the Galerkin Method: The Finite-Element Case","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2156538787","doi":"https://doi.org/10.1137/s0036142998335893","mag":"2156538787"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998335893","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335893","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/A5036192142","display_name":"Bosco Garc\u0131\u0301a-Archilla","orcid":"https://orcid.org/0000-0002-4503-8972"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]},{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Bosco Garc\u00cda-Archilla","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain","Escuela Superior de Ingenieror, Camino de lor Descubrimientor S/N, 41092 Sevilla (Spain)","Matematica Aplicada II, Universidad de Sevilla,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]},{"raw_affiliation_string":"Escuela Superior de Ingenieror, Camino de lor Descubrimientor S/N, 41092 Sevilla (Spain)","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Matematica Aplicada II, Universidad de Sevilla,","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076835339","display_name":"Edriss S. Titi","orcid":"https://orcid.org/0000-0002-5004-1746"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]},{"id":"https://openalex.org/I4210140791","display_name":"Irvine University","ror":"https://ror.org/04ysmca02","country_code":"US","type":"education","lineage":["https://openalex.org/I4210140791"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edriss S. Titi","raw_affiliation_strings":["Department of Mathematics and Department of Mechanical and Aerospace Engineering, Uni-versity of California, Irvine, CA 92697-3875"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Mechanical and Aerospace Engineering, Uni-versity of California, Irvine, CA 92697-3875","institution_ids":["https://openalex.org/I204250578","https://openalex.org/I4210140791"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7066,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.95202593,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"37","issue":"2","first_page":"470","last_page":"499"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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/finite-element-method","display_name":"Finite element method","score":0.7910612225532532},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7729377746582031},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7296335697174072},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6786273717880249},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5661869645118713},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5455538630485535},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5258337259292603},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5232174396514893},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.49037742614746094},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47375163435935974},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4354715049266815},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.4253278374671936},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4213634729385376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38537105917930603},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18149018287658691},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14251026511192322}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7910612225532532},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7729377746582031},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7296335697174072},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6786273717880249},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5661869645118713},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5455538630485535},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5258337259292603},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5232174396514893},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.49037742614746094},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47375163435935974},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4354715049266815},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.4253278374671936},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4213634729385376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38537105917930603},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18149018287658691},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14251026511192322},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142998335893","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998335893","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:dnet:idus________::c645eea8c68cb6f30f1f19091c4713a3","is_oa":false,"landing_page_url":"https://idus.us.es/handle/11441/57580","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W62728038","https://openalex.org/W1557040331","https://openalex.org/W1559403043","https://openalex.org/W1560060148","https://openalex.org/W1562360371","https://openalex.org/W1564341447","https://openalex.org/W1594759473","https://openalex.org/W1595515622","https://openalex.org/W1955535265","https://openalex.org/W1965460593","https://openalex.org/W1966901194","https://openalex.org/W1970723296","https://openalex.org/W1972577443","https://openalex.org/W1972678937","https://openalex.org/W1975664127","https://openalex.org/W1980194259","https://openalex.org/W1980455776","https://openalex.org/W1983786109","https://openalex.org/W1986988877","https://openalex.org/W1991557175","https://openalex.org/W1995504856","https://openalex.org/W1995551283","https://openalex.org/W2004242099","https://openalex.org/W2005601391","https://openalex.org/W2017786109","https://openalex.org/W2020329650","https://openalex.org/W2022980663","https://openalex.org/W2023743841","https://openalex.org/W2041523977","https://openalex.org/W2041999024","https://openalex.org/W2045906052","https://openalex.org/W2058525241","https://openalex.org/W2059874690","https://openalex.org/W2062860872","https://openalex.org/W2073370369","https://openalex.org/W2076699659","https://openalex.org/W2078707336","https://openalex.org/W2091680275","https://openalex.org/W2095377493","https://openalex.org/W2163694039","https://openalex.org/W2282314551","https://openalex.org/W2333052813","https://openalex.org/W2535973907","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2162026849","https://openalex.org/W4238937692","https://openalex.org/W2037688108","https://openalex.org/W2394687667","https://openalex.org/W2548490812","https://openalex.org/W2927373829","https://openalex.org/W2565231037","https://openalex.org/W2376732695","https://openalex.org/W4234704706","https://openalex.org/W2073705841"],"abstract_inverted_index":{"A":[0],"postprocessing":[1,22],"technique,":[2],"developed":[3],"earlier":[4],"for":[5,15],"spectral":[6],"methods,":[7],"is":[8,45,60,64,83,93,124],"extended":[9],"here":[10,76],"to":[11,24,57,90],"Galerkin":[12],"finite-element":[13,55],"methods":[14,103],"dissipative":[16],"evolution":[17],"partial":[18],"differential":[19],"equations.":[20],"The":[21,72,117],"amounts":[23],"solving":[25],"a":[26,31],"linear":[27],"elliptic":[28],"problem":[29],"on":[30,41],"finer":[32],"grid":[33],"(or":[34],"higher-order":[35],"space)":[36],"once":[37],"the":[38,42,50,54,79,88,110,121],"time":[39],"integration":[40],"coarser":[43],"mesh":[44],"completed.":[46],"This":[47],"technique":[48],"increases":[49],"convergence":[51,108],"rate":[52],"of":[53,104,107,120],"method":[56,82,89,123],"which":[58,91],"it":[59,92],"applied,":[61],"and":[62,128],"this":[63],"done":[65],"at":[66],"almost":[67],"no":[68],"additional":[69],"computational":[70],"cost.":[71],"numerical":[73],"experiments":[74],"presented":[75],"show":[77],"that":[78],"resulting":[80],"postprocessed":[81,111],"computationally":[84],"more":[85],"efficient":[86],"than":[87],"applied":[94],"(say,":[95,113],"quadratic":[96],"finite":[97,115],"elements)":[98],"as":[99,101,109],"well":[100],"standard":[102],"similar":[105],"order":[106],"one":[112],"cubic":[114],"elements).":[116],"error":[118],"analysis":[119],"new":[122],"performed":[125],"in":[126,129],"L2":[127],"$L^\\infty$":[130],"norms.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}