{"id":"https://openalex.org/W2128294239","doi":"https://doi.org/10.1002/nme.1620320203","title":"Petrov\u2010Galerkin finite element model for compressible flows","display_name":"Petrov\u2010Galerkin finite element model for compressible flows","publication_year":1991,"publication_date":"1991-08-05","ids":{"openalex":"https://openalex.org/W2128294239","doi":"https://doi.org/10.1002/nme.1620320203","mag":"2128294239"},"language":"en","primary_location":{"id":"doi:10.1002/nme.1620320203","doi":"https://doi.org/10.1002/nme.1620320203","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.1620320203","pdf_url":null,"source":{"id":"https://openalex.org/S165651092","display_name":"International Journal for Numerical Methods in Engineering","issn_l":"0029-5981","issn":["0029-5981","1097-0207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Numerical Methods in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5041941921","display_name":"Frank P. Brueckner","orcid":"https://orcid.org/0000-0003-4373-3848","observed_orcids":["https://orcid.org/0000-0003-4373-3848"]},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frank P. Brueckner","raw_affiliation_strings":["Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona 85721, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona 85721, U.S.A","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111372371","display_name":"Juan C. Heinrich","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juan C. Heinrich","raw_affiliation_strings":["Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona 85721, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona 85721, U.S.A","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":{"value":4250,"currency":"USD","value_usd":4250},"apc_paid":null,"fwci":2.5766,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.897287,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"32","issue":"2","first_page":"255","last_page":"274"},"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":0.9696999788284302,"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":0.9696999788284302,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.029899999499320984,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/petrov-galerkin-method","display_name":"Petrov-Galerkin method","score":0.9789999723434448},{"id":"https://openalex.org/keywords/compressible-flow","display_name":"compressible flow","score":0.8930000066757202},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.890999972820282},{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":1.0},{"id":"https://openalex.org/keywords/scalar-transport","display_name":"scalar transport","score":0.7850000262260437},{"id":"https://openalex.org/keywords/runge-kutta-integration","display_name":"Runge-Kutta time integration","score":0.7250000238418579},{"id":"https://openalex.org/keywords/bilinear-elements","display_name":"bilinear elements","score":0.8009999990463257},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.7289999723434448},{"id":"https://openalex.org/keywords/approximation-properties","display_name":"approximation properties","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6380427479743958},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6344137191772461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6304203271865845},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6161180734634399},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6144943237304688},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5504230260848999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5426559448242188},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5378515124320984},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5056405067443848},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5027763843536377},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.46043911576271057},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.4134068489074707},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36697226762771606},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28211507201194763},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15777966380119324},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12997719645500183},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nme.1620320203","doi":"https://doi.org/10.1002/nme.1620320203","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nme.1620320203","pdf_url":null,"source":{"id":"https://openalex.org/S165651092","display_name":"International Journal for Numerical Methods in Engineering","issn_l":"0029-5981","issn":["0029-5981","1097-0207"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal for Numerical Methods in Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W373462243","https://openalex.org/W1500705422","https://openalex.org/W1556500699","https://openalex.org/W1653855882","https://openalex.org/W1970212576","https://openalex.org/W1970494196","https://openalex.org/W1975961474","https://openalex.org/W1977899298","https://openalex.org/W1985585202","https://openalex.org/W1987971235","https://openalex.org/W1999399767","https://openalex.org/W2003972519","https://openalex.org/W2005350372","https://openalex.org/W2016277211","https://openalex.org/W2024804984","https://openalex.org/W2026229679","https://openalex.org/W2045793197","https://openalex.org/W2071512665","https://openalex.org/W2073897969","https://openalex.org/W2093322335","https://openalex.org/W2095021256","https://openalex.org/W2096271563","https://openalex.org/W2109911863","https://openalex.org/W2118164170","https://openalex.org/W2127453362","https://openalex.org/W2144502017","https://openalex.org/W2749486094","https://openalex.org/W2978957278","https://openalex.org/W4236597200","https://openalex.org/W4302037916","https://openalex.org/W4402311281"],"related_works":["https://openalex.org/W1610724446","https://openalex.org/W1985585202","https://openalex.org/W3020155168","https://openalex.org/W300393892","https://openalex.org/W2791436991","https://openalex.org/W2189207229","https://openalex.org/W2784400113","https://openalex.org/W2024682557","https://openalex.org/W1964938085","https://openalex.org/W290356079"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"Petrov\u2010Galerkin":[2],"method":[3],"for":[4,70],"the":[5,8,20,28,31,37,45,54,57,100,106],"solution":[6],"of":[7,22,30,34,36,56,90,105],"compressible":[9],"Euler":[10,85],"and":[11,53,86,98,102],"Navier\u2010Stokes":[12],"equations":[13],"is":[14,17,48,50,60,68],"presented.":[15],"It":[16],"based":[18],"on":[19],"introduction":[21],"an":[23],"anisotropic":[24,46],"blancing":[25],"diffusion":[26,47,59],"in":[27,43,92],"direction":[29,33,42],"local":[32,41],"propagation":[35],"scalar":[38],"variables.":[39],"The":[40,74],"which":[44],"introduced":[49],"uniquely":[51],"determined,":[52],"magnitude":[55],"balancing":[58],"automatically":[61],"calculated":[62],"locally":[63],"using":[64,79],"a":[65],"criterion":[66],"that":[67],"optimal":[69],"one\u2010dimensional":[71],"transport":[72],"equations.":[73],"algorithm":[75],"has":[76],"been":[77],"implemented":[78],"four\u2010noded":[80],"bilinear":[81],"elements":[82],"with":[83],"forward":[84],"second\u2010order":[87],"Runge\u2010Kutta":[88],"methods":[89],"integration":[91],"time.":[93],"Several":[94],"applications":[95],"are":[96],"presented":[97],"show":[99],"stability":[101],"approximation":[103],"properties":[104],"method.":[107]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}