{"id":"https://openalex.org/W2792767654","doi":"https://doi.org/10.1515/cmam-2018-0006","title":"Trefftz Discontinuous Galerkin Method for Friedrichs Systems with Linear Relaxation: Application to the <i>P</i> <sub>1</sub> Model","display_name":"Trefftz Discontinuous Galerkin Method for Friedrichs Systems with Linear Relaxation: Application to the <i>P</i> <sub>1</sub> Model","publication_year":2018,"publication_date":"2018-03-22","ids":{"openalex":"https://openalex.org/W2792767654","doi":"https://doi.org/10.1515/cmam-2018-0006","mag":"2792767654"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0006","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5108653342","display_name":"Guillaume Morel","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210101455","display_name":"CEA DAM \u00cele-de-France","ror":"https://ror.org/00kn4eb29","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210101455"]},{"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":"Guillaume Morel","raw_affiliation_strings":["CEA , DAM , DIF , 91297 Arpajon ; and Laboratoire Jacques-Louis Lions, UMR 7598, Universit\u00e9 Pierre et Marie Curie (Paris VI), 75005 Paris , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA , DAM , DIF , 91297 Arpajon ; and Laboratoire Jacques-Louis Lions, UMR 7598, Universit\u00e9 Pierre et Marie Curie (Paris VI), 75005 Paris , France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I39804081","https://openalex.org/I2738703131","https://openalex.org/I4210101455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030880733","display_name":"Christophe Buet","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210101455","display_name":"CEA DAM \u00cele-de-France","ror":"https://ror.org/00kn4eb29","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210101455"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Buet","raw_affiliation_strings":["CEA , DAM , DIF , 91297 Arpajon , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA , DAM , DIF , 91297 Arpajon , France","institution_ids":["https://openalex.org/I4210101455","https://openalex.org/I2738703131"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113826510","display_name":"Bruno Despr\u00e9s","orcid":null},"institutions":[{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"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":false,"raw_author_name":"Bruno Despres","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, UMR 7598 , Universit\u00e9 Pierre et Marie Curie (Paris VI) , 75005 Paris ; and Institut Universitaire de France , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, UMR 7598 , Universit\u00e9 Pierre et Marie Curie (Paris VI) , 75005 Paris ; and Institut Universitaire de France , France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I185839726","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108653342"],"corresponding_institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I39804081","https://openalex.org/I4210101455","https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":0.8326,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69208996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"3","first_page":"521","last_page":"557"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/dimension","display_name":"Dimension (graph theory)","score":0.6563160419464111},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6414122581481934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5521845817565918},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5096578598022461},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5074076056480408},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4596547484397888},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.45761838555336},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35714441537857056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31526991724967957},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.213811457157135},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16554737091064453},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06618016958236694}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6563160419464111},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6414122581481934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5521845817565918},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5096578598022461},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5074076056480408},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4596547484397888},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.45761838555336},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35714441537857056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31526991724967957},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.213811457157135},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16554737091064453},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06618016958236694},{"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/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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0006","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0006","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W269028348","https://openalex.org/W295174034","https://openalex.org/W1480149586","https://openalex.org/W1758897595","https://openalex.org/W1943976203","https://openalex.org/W1964245657","https://openalex.org/W1967469744","https://openalex.org/W1976156411","https://openalex.org/W1978508895","https://openalex.org/W1978561325","https://openalex.org/W1979771104","https://openalex.org/W1988079050","https://openalex.org/W2013637933","https://openalex.org/W2029725158","https://openalex.org/W2033675399","https://openalex.org/W2073333791","https://openalex.org/W2073370219","https://openalex.org/W2074597100","https://openalex.org/W2077458918","https://openalex.org/W2092011174","https://openalex.org/W2093151475","https://openalex.org/W2097144461","https://openalex.org/W2099993874","https://openalex.org/W2127600768","https://openalex.org/W2150323068","https://openalex.org/W2156695289","https://openalex.org/W2165335881","https://openalex.org/W2168644075","https://openalex.org/W2209880586","https://openalex.org/W2281918920","https://openalex.org/W2355562509","https://openalex.org/W2478955545","https://openalex.org/W3104755947","https://openalex.org/W3135227555","https://openalex.org/W3204708751","https://openalex.org/W4296942791","https://openalex.org/W4309680536","https://openalex.org/W6600704223"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W2324487000"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"work":[2],"deals":[3],"with":[4,18,91,103],"the":[5,51,69,86,94,104,128],"first":[6],"Trefftz":[7],"Discontinuous":[8],"Galerkin":[9],"(TDG)":[10],"scheme":[11],"for":[12,107],"a":[13,26],"model":[14,21,60,116],"problem":[15,22],"of":[16],"transport":[17],"relaxation.":[19],"The":[20],"is":[23,100],"written":[24],"as":[25],"<m:math":[27,36,52,108],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[28,37,53,109],"<m:msub>":[29,38,54,110],"<m:mi>P</m:mi>":[30,55,111],"<m:mi>N</m:mi>":[31,40],"</m:msub>":[32,41,57,113],"</m:math>":[33,42,58,114],"{P_{N}}":[34],"or":[35],"<m:mi>S</m:mi>":[39],"{S_{N}}":[43],"model,":[44],"and":[45,64,75,125],"we":[46],"study":[47],"in":[48,61,85,97,117,122],"more":[49],"details":[50],"<m:mn>1</m:mn>":[56,112],"{P_{1}}":[59,115],"dimension":[62,118],"1":[63,124],"2.":[65],"We":[66],"show":[67],"that":[68],"TDG":[70],"method":[71],"provides":[72],"natural":[73],"well-balanced":[74],"asymptotic":[76,105],"preserving":[77],"discretization":[78],"since":[79],"exact":[80],"solutions":[81],"are":[82],"used":[83],"locally":[84],"basis":[87],"functions.":[88],"High-order":[89],"convergence":[90],"respect":[92],"to":[93],"mesh":[95],"size":[96],"two":[98],"dimensions":[99,123],"proved":[101],"together":[102],"property":[106],"one.":[119],"Numerical":[120],"results":[121],"2":[126],"illustrate":[127],"theoretical":[129],"properties.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}