{"id":"https://openalex.org/W2133572972","doi":"https://doi.org/10.1137/15m1046265","title":"A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws","display_name":"A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2133572972","doi":"https://doi.org/10.1137/15m1046265","mag":"2133572972"},"language":"en","primary_location":{"id":"doi:10.1137/15m1046265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1046265","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.05430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andreas Dedner","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andreas Dedner","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Jan Giesselmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jan Giesselmann","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9257,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.72494345,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"6","first_page":"3523","last_page":"3549"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.42089998722076416,"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":0.42089998722076416,"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":0.3659000098705292,"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":0.05050000175833702,"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/conservation-law","display_name":"Conservation law","score":0.8238999843597412},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7698000073432922},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7084000110626221},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.531000018119812},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.48339998722076416},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4050999879837036},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.3955000042915344},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3919000029563904}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8238999843597412},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7698000073432922},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684999704360962},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7084000110626221},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5974000096321106},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.531000018119812},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.48339998722076416},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4278999865055084},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3955000042915344},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3919000029563904},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.383899986743927},{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.36719998717308044},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C152284280","wikidata":"https://www.wikidata.org/wiki/Q7828154","display_name":"Total variation diminishing","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.31150001287460327},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2896000146865845},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2599000036716461},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1046265","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1046265","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:wrap.warwick.ac.uk:81906","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:1510.05430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.05430","pdf_url":"https://arxiv.org/pdf/1510.05430","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1510.05430","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.05430","pdf_url":"https://arxiv.org/pdf/1510.05430","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8366892933","display_name":null,"funder_award_id":"SFB TRR 75","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"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":28,"referenced_works":["https://openalex.org/W1969122636","https://openalex.org/W1972971898","https://openalex.org/W1974585782","https://openalex.org/W1980520313","https://openalex.org/W1984588467","https://openalex.org/W1987166016","https://openalex.org/W1993006253","https://openalex.org/W1996082552","https://openalex.org/W1996850377","https://openalex.org/W2016356237","https://openalex.org/W2023113756","https://openalex.org/W2026229679","https://openalex.org/W2028967809","https://openalex.org/W2037701755","https://openalex.org/W2040415781","https://openalex.org/W2042118059","https://openalex.org/W2044846554","https://openalex.org/W2072640387","https://openalex.org/W2091396657","https://openalex.org/W2097509761","https://openalex.org/W2112005197","https://openalex.org/W2121296933","https://openalex.org/W2125123420","https://openalex.org/W2128506141","https://openalex.org/W2138882090","https://openalex.org/W4231817347","https://openalex.org/W4232713875","https://openalex.org/W4233070363"],"related_works":[],"abstract_inverted_index":{"We":[0,128,153,208],"present":[1,62],"reliable":[2],"a":[3,32,55,63,198],"posteriori":[4],"estimators":[5,53],"for":[6,59,68,88,122,179],"some":[7,211],"fully":[8],"discrete":[9,133],"schemes":[10,28],"applied":[11],"to":[12,75,98,112,144,192,197,214],"nonlinear":[13],"systems":[14],"of":[15,34,51,107,125,131,150,165,200,218],"hyperbolic":[16],"conservation":[17,76,114],"laws":[18],"in":[19,47,57,92,96,147],"one":[20],"space":[21],"dimension":[22],"with":[23,42,136,210],"strictly":[24],"convex":[25],"entropy.":[26],"The":[27,49,78],"are":[29],"based":[30],"on":[31,83,158],"method":[33,86],"lines":[35],"approach":[36,74],"combining":[37],"discontinuous":[38],"Galerkin":[39],"spatial":[40,118],"discretization":[41],"single-":[43],"or":[44],"multi-step":[45],"methods":[46,100,109],"time.":[48,93],"construction":[50],"the":[52,73,84,90,104,117,132,137,148,159,162,170,188,201,216,219],"requires":[54],"reconstruction":[56,79],"time":[58],"which":[60,142,156],"we":[61,120,172],"very":[64],"general":[65],"framework":[66,204],"first":[67],"ODEs":[69],"and":[70,176],"then":[71],"applying":[72],"laws.":[77,115],"does":[80],"not":[81],"depend":[82],"actual":[85],"used":[87,111],"evolving":[89],"solution":[91,134],"Most":[94],"importantly,":[95],"addition":[97],"implicit":[99],"it":[101,183],"also":[102],"covers":[103],"wide":[105],"range":[106],"explicit":[108],"typically":[110],"solve":[113],"For":[116],"discretization,":[119],"allow":[121],"standard":[123],"choices":[124],"numerical":[126,160,212],"fluxes.":[127],"use":[129],"reconstructions":[130],"together":[135],"relative":[138,202],"entropy":[139,203],"stability":[140],"framework,":[141],"leads":[143],"error":[145],"control":[146],"case":[149],"smooth":[151],"solutions.":[152],"study":[154],"under":[155],"conditions":[157],"flux":[161],"estimate":[163],"is":[164,174,195],"optimal":[166],"order":[167],"preshock.":[168],"While":[169],"estimator":[171],"derive":[173],"computable":[175],"valid":[177],"postshock":[178],"fixed":[180],"mesh":[181,189],"size,":[182],"will":[184],"blow":[185],"up":[186],"as":[187],"size":[190],"tends":[191],"zero.":[193],"This":[194],"due":[196],"breakdown":[199],"when":[205],"discontinuities":[206],"develop.":[207],"conclude":[209],"benchmarking":[213],"test":[215],"robustness":[217],"derived":[220],"estimator.":[221]},"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}
