{"id":"https://openalex.org/W1986675731","doi":"https://doi.org/10.1137/110848815","title":"Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems","display_name":"Fast Relaxation Solvers for Hyperbolic-Elliptic Phase Transition Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1986675731","doi":"https://doi.org/10.1137/110848815","mag":"1986675731"},"language":"en","primary_location":{"id":"doi:10.1137/110848815","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110848815","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5109963934","display_name":"Ch. Chalons","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ch. Chalons","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113797855","display_name":"Fr\u00e9\u0301d\u00e9\u0301ric Coquel","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. Coquel","raw_affiliation_strings":["Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique"],"affiliations":[{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, \u00c9cole Polytechnique","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073496723","display_name":"Pablo Engel","orcid":"https://orcid.org/0000-0001-8410-252X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Engel","raw_affiliation_strings":["Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart]"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart]","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106418780","display_name":"Ch. Rohde","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ch. Rohde","raw_affiliation_strings":["Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart]"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Analysis und Numerische Simulation [Stuttgart]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109963934"],"corresponding_institution_ids":["https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":3.8425,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.92734311,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"34","issue":"3","first_page":"A1753","last_page":"A1776"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/riemann-problem","display_name":"Riemann problem","score":0.8584549427032471},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7280069589614868},{"id":"https://openalex.org/keywords/riemann-solver","display_name":"Riemann solver","score":0.6781772971153259},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5970605611801147},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5838353633880615},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5464436411857605},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4752602279186249},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4641875624656677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4289957284927368},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.1820800006389618},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12277618050575256}],"concepts":[{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.8584549427032471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7280069589614868},{"id":"https://openalex.org/C120796332","wikidata":"https://www.wikidata.org/wiki/Q6153788","display_name":"Riemann solver","level":3,"score":0.6781772971153259},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5970605611801147},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5838353633880615},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5464436411857605},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4752602279186249},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4641875624656677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4289957284927368},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.1820800006389618},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12277618050575256},{"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110848815","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110848815","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W285505819","https://openalex.org/W334267536","https://openalex.org/W348217116","https://openalex.org/W392206547","https://openalex.org/W1533568430","https://openalex.org/W1969402902","https://openalex.org/W1974079461","https://openalex.org/W1981825355","https://openalex.org/W1985570727","https://openalex.org/W1987258148","https://openalex.org/W1991090172","https://openalex.org/W2002544802","https://openalex.org/W2005419851","https://openalex.org/W2005502967","https://openalex.org/W2017935165","https://openalex.org/W2018936145","https://openalex.org/W2029541243","https://openalex.org/W2038157636","https://openalex.org/W2046494788","https://openalex.org/W2048459778","https://openalex.org/W2049647698","https://openalex.org/W2052667560","https://openalex.org/W2060976754","https://openalex.org/W2062845250","https://openalex.org/W2071115019","https://openalex.org/W2071816708","https://openalex.org/W2073447845","https://openalex.org/W2074633665","https://openalex.org/W2077061939","https://openalex.org/W2078665336","https://openalex.org/W2100669199","https://openalex.org/W2120005033","https://openalex.org/W2137742686","https://openalex.org/W2165182409","https://openalex.org/W2167278920","https://openalex.org/W2963773710"],"related_works":["https://openalex.org/W3195766120","https://openalex.org/W569491316","https://openalex.org/W2036623811","https://openalex.org/W3174853118","https://openalex.org/W2379245068","https://openalex.org/W2142702340","https://openalex.org/W2020017862","https://openalex.org/W2161856882","https://openalex.org/W2133986346","https://openalex.org/W4385807557"],"abstract_inverted_index":{"Phase":[0],"transition":[1],"problems":[2],"in":[3,93,124,184],"compressible":[4],"media":[5],"can":[6],"be":[7],"modelled":[8],"by":[9],"mixed":[10],"hyperbolic-elliptic":[11,82],"systems":[12],"of":[13,45,51,77,130],"conservation":[14],"laws.":[15],"Within":[16],"this":[17,71],"approach":[18,132],"phase":[19,99,106],"boundaries":[20,100],"are":[21,63,122,147],"understood":[22],"as":[23],"shock":[24],"waves":[25],"that":[26,84],"satisfy":[27],"additional":[28],"constraints,":[29],"sometimes":[30],"called":[31],"kinetic":[32,57,96,141,152],"relations.":[33],"For":[34,149],"numerical":[35],"approximation":[36],"tracking-type":[37],"algorithms":[38,47],"have":[39],"been":[40],"suggested.":[41],"The":[42,128],"core":[43],"piece":[44],"these":[46,185],"is":[48,133,180],"the":[49,56,95,108,118,125,131,160,167],"usage":[50],"exact":[52,60,144,174],"Riemann":[53,61,79,120,145,168,178],"solvers":[54,62,80,121,146],"incorporating":[55],"relation.":[58],"However,":[59],"computationally":[64],"expensive":[65],"or":[66],"even":[67],"not":[68,182],"available.":[69,148],"In":[70,111],"paper":[72],"we":[73,158],"present":[74],"a":[75,87,114,136,150,155],"class":[76],"approximate":[78,119],"for":[81,98,104,176],"models":[83],"relies":[85],"on":[86,135,166],"generalized":[88],"relaxation":[89],"procedure.":[90],"It":[91],"preserves":[92],"particular":[94],"relation":[97,142,153],"exactly":[101],"and":[102,154],"gives":[103],"isolated":[105],"transitions":[107],"correct":[109],"solutions.":[110],"combination":[112],"with":[113,139],"novel":[115],"subiteration":[116],"procedure":[117],"used":[123],"tracking":[126],"algorithms.":[127],"efficiency":[129],"validated":[134],"barotropic":[137],"system":[138,157],"linear":[140],"where":[143],"nonlinear":[151],"thermoelastic":[156],"use":[159],"new":[161],"method":[162],"to":[163],"gain":[164],"information":[165],"problem.":[169],"To":[170],"our":[171],"knowledge":[172],"an":[173],"solution":[175],"arbitrary":[177],"data":[179],"currently":[181],"available":[183],"cases.":[186]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}