{"id":"https://openalex.org/W2938404122","doi":"https://doi.org/10.1515/cmam-2019-0060","title":"The Gradient Discretisation Method for Linear Advection Problems","display_name":"The Gradient Discretisation Method for Linear Advection Problems","publication_year":2019,"publication_date":"2019-10-17","ids":{"openalex":"https://openalex.org/W2938404122","doi":"https://doi.org/10.1515/cmam-2019-0060","mag":"2938404122"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2019-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2019-0060","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.12415","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075602113","display_name":"J\u00e9r\u00f4me Droniou","orcid":"https://orcid.org/0000-0002-3339-3053"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Droniou","raw_affiliation_strings":["School of Mathematics , Monash University , Melbourne , Australia"],"raw_orcid":"https://orcid.org/0000-0002-3339-3053","affiliations":[{"raw_affiliation_string":"School of Mathematics , Monash University , Melbourne , Australia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057528055","display_name":"Robert Eymard","orcid":"https://orcid.org/0000-0002-6035-0104"},"institutions":[{"id":"https://openalex.org/I4210144844","display_name":"Laboratoire d\u2019Analyse et de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/0581g8849","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210141950","https://openalex.org/I4210144844","https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Robert Eymard","raw_affiliation_strings":["LAMA , Universit\u00e9 Gustave Eiffel, UPEM , F-77447 Marne-la-Vall\u00e9e , France"],"raw_orcid":"https://orcid.org/0000-0002-6035-0104","affiliations":[{"raw_affiliation_string":"LAMA , Universit\u00e9 Gustave Eiffel, UPEM , F-77447 Marne-la-Vall\u00e9e , France","institution_ids":["https://openalex.org/I4210144844","https://openalex.org/I4210154111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051621649","display_name":"Thierry Gallou\u00ebt","orcid":"https://orcid.org/0000-0002-7037-5751"},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thierry Gallou\u00ebt","raw_affiliation_strings":["Institut de Math\u00e9matiques de Marseille , Aix-Marseille Universit\u00e9 , Marseille , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Marseille , Aix-Marseille Universit\u00e9 , Marseille , France","institution_ids":["https://openalex.org/I4210138206","https://openalex.org/I21491767"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108830760","display_name":"Rapha\u00e8le Herbin","orcid":null},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rapha\u00e8le Herbin","raw_affiliation_strings":["Institut de Math\u00e9matiques de Marseille , Aix-Marseille Universit\u00e9 , Marseille , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Marseille , Aix-Marseille Universit\u00e9 , Marseille , France","institution_ids":["https://openalex.org/I4210138206","https://openalex.org/I21491767"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057528055"],"corresponding_institution_ids":["https://openalex.org/I4210144844","https://openalex.org/I4210154111"],"apc_list":null,"apc_paid":null,"fwci":0.5824,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64264556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"20","issue":"3","first_page":"437","last_page":"458"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9977999925613403,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9909999966621399,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7689043879508972},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7349383234977722},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7206689715385437},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6116069555282593},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.5705963373184204},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5155327320098877},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5096113681793213},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.47590765357017517},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4758695960044861},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.45288822054862976},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.447447806596756},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.42813020944595337},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4152665436267853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2583649158477783},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14754435420036316},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1277288794517517},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07761338353157043}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7689043879508972},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7349383234977722},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7206689715385437},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6116069555282593},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.5705963373184204},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5155327320098877},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5096113681793213},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.47590765357017517},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4758695960044861},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45288822054862976},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.447447806596756},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.42813020944595337},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4152665436267853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2583649158477783},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14754435420036316},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1277288794517517},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07761338353157043},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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:10.1515/cmam-2019-0060","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2019-0060","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"},{"id":"pmh:oai:arXiv.org:1903.12415","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.12415","pdf_url":"https://arxiv.org/pdf/1903.12415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.12415","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.12415","pdf_url":"https://arxiv.org/pdf/1903.12415","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W593406250","https://openalex.org/W612015062","https://openalex.org/W656657393","https://openalex.org/W1257148767","https://openalex.org/W1549748890","https://openalex.org/W1555674425","https://openalex.org/W1601728065","https://openalex.org/W1964504217","https://openalex.org/W2014282047","https://openalex.org/W2018264669","https://openalex.org/W2021867586","https://openalex.org/W2038490905","https://openalex.org/W2042321858","https://openalex.org/W2044670314","https://openalex.org/W2065438814","https://openalex.org/W2068039185","https://openalex.org/W2091156165","https://openalex.org/W2125529818","https://openalex.org/W2138583506","https://openalex.org/W2276594788","https://openalex.org/W2289366489","https://openalex.org/W2514850036","https://openalex.org/W2735433906","https://openalex.org/W2790754607","https://openalex.org/W2885405756","https://openalex.org/W3020991820","https://openalex.org/W3046567100","https://openalex.org/W3112330256","https://openalex.org/W3121669256","https://openalex.org/W4205793979"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2087496541","https://openalex.org/W2028455732","https://openalex.org/W4313703117","https://openalex.org/W2085564391","https://openalex.org/W1984758362","https://openalex.org/W2034255721","https://openalex.org/W2032446390","https://openalex.org/W4387214872"],"abstract_inverted_index":{"Abstract":[0],"We":[1,85],"adapt":[2],"the":[3,18,28,40,87,95,112],"Gradient":[4],"Discretisation":[5],"Method":[6],"(GDM),":[7],"originally":[8],"designed":[9],"for":[10,68],"elliptic":[11],"and":[12,31,63,106,110],"parabolic":[13],"partial":[14],"differential":[15],"equations,":[16],"to":[17,39,43],"case":[19],"of":[20,34,75],"a":[21],"linear":[22,80],"scalar":[23],"hyperbolic":[24],"equations.":[25],"This":[26],"enables":[27],"simultaneous":[29],"design":[30],"convergence":[32,88],"analysis":[33,89],"various":[35],"numerical":[36,83,91],"schemes,":[37],"corresponding":[38],"methods":[41,66],"known":[42],"be":[44],"GDMs,":[45],"such":[46],"as":[47],"finite":[48,56,108,114],"elements":[49],"(conforming":[50],"or":[51,54,60,81],"non-conforming,":[52],"standard":[53],"mass-lumped),":[55],"volumes":[57],"on":[58,94,111],"rectangular":[59],"simplicial":[61],"grids,":[62],"other":[64],"recent":[65],"developed":[67],"general":[69],"polytopal":[70],"meshes.":[71],"The":[72],"scheme":[73],"is":[74],"centred":[76],"type,":[77],"with":[78,90],"added":[79],"non-linear":[82],"diffusion.":[84],"complement":[86],"tests":[92],"based":[93],"mass-lumped":[96],"<m:math":[97],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[98],"<m:msub>":[99],"<m:mi>\u2119</m:mi>":[100],"<m:mn>1</m:mn>":[101],"</m:msub>":[102],"</m:math>":[103],"{\\mathbb{P}_{1}}":[104],"conforming":[105],"non-conforming":[107],"element":[109],"hybrid":[113],"volume":[115],"method.":[116]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}