{"id":"https://openalex.org/W2018695612","doi":"https://doi.org/10.1137/060664872","title":"High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems","display_name":"High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2018695612","doi":"https://doi.org/10.1137/060664872","mag":"2018695612"},"language":"en","primary_location":{"id":"doi:10.1137/060664872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060664872","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2318/92485","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013817442","display_name":"Fausto Cavalli","orcid":"https://orcid.org/0000-0002-3931-7684"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fausto Cavalli","raw_affiliation_strings":["University of Milan"],"affiliations":[{"raw_affiliation_string":"University of Milan","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062399881","display_name":"Giovanni Naldi","orcid":"https://orcid.org/0000-0001-9191-6003"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Naldi","raw_affiliation_strings":["University of Milan"],"affiliations":[{"raw_affiliation_string":"University of Milan","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033971904","display_name":"Gabriella Puppo","orcid":"https://orcid.org/0000-0003-3953-5566"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Polytechnic University of Turin","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gabriella Puppo","raw_affiliation_strings":["POLYTECHNIC UNIVERSITY OF TURIN"],"affiliations":[{"raw_affiliation_string":"POLYTECHNIC UNIVERSITY OF TURIN","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063991804","display_name":"Matteo Semplice","orcid":"https://orcid.org/0000-0002-2398-0828"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Matteo Semplice","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Milano,Via Saldini 50, I-20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Milano,Via Saldini 50, I-20133 Milano, Italy","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5013817442"],"corresponding_institution_ids":["https://openalex.org/I189158943"],"apc_list":null,"apc_paid":null,"fwci":3.4278,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.9144673,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"5","first_page":"2098","last_page":"2119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973000288009644,"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/T11416","display_name":"Numerical methods for differential equations","score":0.994700014591217,"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/mathematics","display_name":"Mathematics","score":0.7939531803131104},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7753652334213257},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.6893056035041809},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6710172295570374},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6475629806518555},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5920632481575012},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5656821131706238},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5656809210777283},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.485708087682724},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48328712582588196},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.48091694712638855},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.44521600008010864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4010707437992096},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.2640454173088074}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7939531803131104},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7753652334213257},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.6893056035041809},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6710172295570374},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6475629806518555},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5920632481575012},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5656821131706238},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5656809210777283},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.485708087682724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48328712582588196},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.48091694712638855},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.44521600008010864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4010707437992096},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.2640454173088074},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/060664872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060664872","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:iris.unito.it:2318/92485","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/92485","pdf_url":"http://hdl.handle.net/2318/92485","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.6652","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.6652","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0604572v2.pdf","raw_type":"text"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/1789566","is_oa":false,"landing_page_url":"http://hdl.handle.net/11383/1789566","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/1280488","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/1280488","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unito.it:2318/92485","is_oa":true,"landing_page_url":"http://hdl.handle.net/2318/92485","pdf_url":"http://hdl.handle.net/2318/92485","source":{"id":"https://openalex.org/S4306400637","display_name":"Institutional Research Information System University of Turin (University of Turin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I55143463","host_organization_name":"University of Turin","host_organization_lineage":["https://openalex.org/I55143463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.7200000286102295,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018695612.pdf"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W192052997","https://openalex.org/W328073187","https://openalex.org/W1480546554","https://openalex.org/W1528848089","https://openalex.org/W1584428886","https://openalex.org/W1886421468","https://openalex.org/W1966058908","https://openalex.org/W1970805553","https://openalex.org/W1973481688","https://openalex.org/W1984125253","https://openalex.org/W1985554304","https://openalex.org/W1991903386","https://openalex.org/W2010506467","https://openalex.org/W2013637933","https://openalex.org/W2016911123","https://openalex.org/W2017620052","https://openalex.org/W2017883116","https://openalex.org/W2022022697","https://openalex.org/W2022770433","https://openalex.org/W2035930403","https://openalex.org/W2036278786","https://openalex.org/W2037004033","https://openalex.org/W2040044288","https://openalex.org/W2051165327","https://openalex.org/W2054420328","https://openalex.org/W2054982998","https://openalex.org/W2059328025","https://openalex.org/W2060976754","https://openalex.org/W2061143360","https://openalex.org/W2064265943","https://openalex.org/W2070621570","https://openalex.org/W2073447845","https://openalex.org/W2074494226","https://openalex.org/W2094559589","https://openalex.org/W2100520965","https://openalex.org/W2116729868","https://openalex.org/W2132678371","https://openalex.org/W2587143772","https://openalex.org/W2765647671","https://openalex.org/W2949689818","https://openalex.org/W2951459038"],"related_works":["https://openalex.org/W2971099291","https://openalex.org/W3099211396","https://openalex.org/W2941405134","https://openalex.org/W4317210689","https://openalex.org/W2886810076","https://openalex.org/W1484269119","https://openalex.org/W126524403","https://openalex.org/W4285445988","https://openalex.org/W3054186628","https://openalex.org/W2374370419"],"abstract_inverted_index":{"Several":[0],"relaxation":[1,29,50],"approximations":[2],"to":[3,131],"partial":[4],"differential":[5],"equations":[6,138],"have":[7],"been":[8],"recently":[9],"proposed.":[10],"Examples":[11],"include":[12],"conservation":[13],"laws,":[14],"Hamilton\u2013Jacobi":[15],"equations,":[16],"convection-diffusion":[17],"problems,":[18],"and":[19,59,77,100,107,129,141],"gas":[20],"dynamics":[21],"problems.":[22],"The":[23],"present":[24],"paper":[25],"focuses":[26],"on":[27,43,126],"diffusive":[28],"schemes":[30,40,64,71,85,121],"for":[31,65,72,83,90],"the":[32,104,111,117],"numerical":[33,88,96,113],"approximation":[34],"of":[35,110,135],"nonlinear":[36,136],"parabolic":[37,137],"equations.":[38],"These":[39,120],"are":[41,54,81],"based":[42],"a":[44,78,87],"suitable":[45],"semilinear":[46],"hyperbolic":[47],"system":[48],"with":[49,68,86],"terms.":[51],"High-order":[52],"methods":[53],"obtained":[55],"by":[56],"coupling":[57],"ENO":[58],"weighted":[60],"essentially":[61],"nonoscillatory":[62],"(WENO)":[63],"space":[66],"discretization":[67],"implicit-explicit":[69],"(IMEX)":[70],"time":[73],"integration.":[74],"Error":[75],"estimates":[76],"convergence":[79],"analysis":[80,89],"developed":[82],"semidiscrete":[84],"fully":[91],"discrete":[92],"relaxed":[93],"schemes.":[94],"Various":[95],"results":[97],"in":[98,116,139],"one":[99],"two":[101],"dimensions":[102],"illustrate":[103],"high":[105],"accuracy":[106],"good":[108],"properties":[109],"proposed":[112],"schemes,":[114],"also":[115],"degenerate":[118],"case.":[119],"can":[122],"be":[123],"easily":[124],"implemented":[125],"parallel":[127],"computers":[128],"applied":[130],"more":[132],"general":[133],"systems":[134],"two-":[140],"three-dimensional":[142],"cases.":[143]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
