{"id":"https://openalex.org/W2997267744","doi":"https://doi.org/10.1137/19m1243798","title":"Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes","display_name":"Discontinuous Galerkin Methods for Nonlinear Scalar Conservation Laws: Generalized Local Lax--Friedrichs Numerical Fluxes","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2997267744","doi":"https://doi.org/10.1137/19m1243798","mag":"2997267744"},"language":"en","primary_location":{"id":"doi:10.1137/19m1243798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1243798","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100405666","display_name":"Jia Li","orcid":"https://orcid.org/0000-0001-7617-1285"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jia Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038068859","display_name":"Dazhi Zhang","orcid":"https://orcid.org/0009-0005-0518-7702"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dazhi Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101428593","display_name":"Xiong Meng","orcid":"https://orcid.org/0000-0003-1071-3787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiong Meng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061700722","display_name":"Boying Wu","orcid":"https://orcid.org/0000-0002-5611-650X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boying Wu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027410721","display_name":"Qiang Zhang","orcid":"https://orcid.org/0000-0003-1796-7042"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiang Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100405666"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5845,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.79441019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"1","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998999834060669,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.8456394672393799},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.7471576929092407},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.745578944683075},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.723320484161377},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6692548394203186},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6114112138748169},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.605624794960022},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5357438921928406},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4939432740211487},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.48880669474601746},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.47079411149024963},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.44863009452819824},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4136032164096832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39542847871780396},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2537631094455719},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20421263575553894},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10144174098968506},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07866466045379639},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.0704571008682251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8456394672393799},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7471576929092407},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.745578944683075},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.723320484161377},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6692548394203186},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6114112138748169},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.605624794960022},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5357438921928406},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4939432740211487},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.48880669474601746},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.47079411149024963},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.44863009452819824},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4136032164096832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39542847871780396},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2537631094455719},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20421263575553894},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10144174098968506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07866466045379639},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.0704571008682251},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1243798","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1243798","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.699999988079071,"id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G1469580534","display_name":null,"funder_award_id":"11671199","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1664889433","display_name":null,"funder_award_id":"11501149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3795778106","display_name":null,"funder_award_id":"2017YFB1401801","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4982802486","display_name":null,"funder_award_id":"71773024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5695924675","display_name":null,"funder_award_id":"11571290","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1791091458","https://openalex.org/W1967575591","https://openalex.org/W1975036160","https://openalex.org/W1987826592","https://openalex.org/W1998017442","https://openalex.org/W1998934494","https://openalex.org/W2014282047","https://openalex.org/W2054766104","https://openalex.org/W2081377160","https://openalex.org/W2083855576","https://openalex.org/W2088938487","https://openalex.org/W2116729868","https://openalex.org/W2218947347","https://openalex.org/W2317341383","https://openalex.org/W2342478278","https://openalex.org/W2507558872","https://openalex.org/W2588568969","https://openalex.org/W2884477368","https://openalex.org/W2892103335","https://openalex.org/W4236438452"],"related_works":["https://openalex.org/W2268950858","https://openalex.org/W4288598778","https://openalex.org/W2114051189","https://openalex.org/W4236183264","https://openalex.org/W2081377160","https://openalex.org/W220460885","https://openalex.org/W2005381510","https://openalex.org/W1629836751","https://openalex.org/W2047042052","https://openalex.org/W1943927944"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,47,80],"study":[4],"the":[5,45,50,53,57,61,76,89,151],"discontinuous":[6],"Galerkin":[7],"(DG)":[8],"method":[9],"with":[10,29,75,92],"a":[11,42,68],"class":[12],"of":[13,60,153],"generalized":[14,24],"numerical":[15,101,137],"fluxes":[16,28,122],"for":[17,44,52,88,99,103,121],"one-dimensional":[18],"scalar":[19],"nonlinear":[20],"conservation":[21],"laws.":[22],"The":[23,95],"local":[25],"Lax--Friedrichs":[26],"(GLLF)":[27],"two":[30],"weights,":[31,46],"which":[32,73,104],"may":[33],"not":[34,125],"be":[35,109],"monotone,":[36,126],"are":[37,81,118,124,147],"proposed":[38],"and":[39,55,66,139],"analyzed.":[40],"Under":[41],"condition":[43],"first":[48],"show":[49,84,150],"monotonicity":[51],"flux":[54],"thus":[56,140],"$L^2$":[58],"stability":[59],"scheme.":[62],"Then,":[63],"by":[64],"constructing":[65],"analyzing":[67],"special":[69],"piecewise":[70],"global":[71],"projection":[72],"commutes":[74],"time":[77],"derivative":[78],"operator,":[79],"able":[82],"to":[83,129,134,141,149],"optimal":[85,115],"error":[86,116],"estimates":[87,107,117],"DG":[90],"scheme":[91],"GLLF":[93],"fluxes.":[94],"result":[96],"is":[97],"sharp":[98],"monotone":[100],"fluxes,":[102],"only":[105],"suboptimal":[106],"can":[108],"proved":[110],"in":[111],"previous":[112],"work.":[113],"Moreover,":[114],"still":[119],"valid":[120],"that":[123],"allowing":[127],"us":[128],"choose":[130],"some":[131],"suitable":[132],"weights":[133],"achieve":[135],"less":[136],"dissipation":[138],"better":[142],"resolve":[143],"shocks.":[144],"Numerical":[145],"experiments":[146],"provided":[148],"sharpness":[152],"theoretical":[154],"results.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}