{"id":"https://openalex.org/W3015004016","doi":"https://doi.org/10.1090/mcom/3550","title":"Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations","display_name":"Analysis of local discontinuous Galerkin methods with generalized numerical fluxes for linearized KdV equations","publication_year":2020,"publication_date":"2020-04-01","ids":{"openalex":"https://openalex.org/W3015004016","doi":"https://doi.org/10.1090/mcom/3550","mag":"3015004016"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3550","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3550","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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":[{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jia Li","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210161462"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038068859","display_name":"Dazhi Zhang","orcid":"https://orcid.org/0009-0005-0518-7702"},"institutions":[{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dazhi Zhang","raw_affiliation_strings":["School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210161462"]},{"raw_affiliation_string":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101428593","display_name":"Xiong Meng","orcid":"https://orcid.org/0000-0003-1071-3787"},"institutions":[{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiong Meng","raw_affiliation_strings":["School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Republic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061700722","display_name":"Boying Wu","orcid":"https://orcid.org/0000-0002-5611-650X"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Boying Wu","raw_affiliation_strings":["School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Repbulic of China","School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Repbulic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People\u00e2\u0080\u0099s Repbulic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]},{"raw_affiliation_string":"School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang, People's Repbulic of China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100405666"],"corresponding_institution_ids":["https://openalex.org/I204983213","https://openalex.org/I4210161462"],"apc_list":null,"apc_paid":null,"fwci":1.4085,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.77602411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"89","issue":"325","first_page":"2085","last_page":"2111"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9990000128746033,"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":0.9990000128746033,"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":0.8393276929855347},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5359680652618408},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.5216617584228516},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4913236200809479},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4759611487388611},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46405330300331116},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44143056869506836},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4367297291755676},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.15059801936149597},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0932302176952362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8393276929855347},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5359680652618408},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.5216617584228516},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4913236200809479},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4759611487388611},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46405330300331116},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44143056869506836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4367297291755676},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.15059801936149597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0932302176952362},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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:10.1090/mcom/3550","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3550","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1767164469","display_name":null,"funder_award_id":"1501149","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8821457016","display_name":null,"funder_award_id":"11971132","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1507767947","https://openalex.org/W1791091458","https://openalex.org/W1975036160","https://openalex.org/W1979283178","https://openalex.org/W1982465309","https://openalex.org/W1993923624","https://openalex.org/W1998934494","https://openalex.org/W2005380085","https://openalex.org/W2012938047","https://openalex.org/W2019767773","https://openalex.org/W2046134068","https://openalex.org/W2065908448","https://openalex.org/W2068634975","https://openalex.org/W2068981255","https://openalex.org/W2074622236","https://openalex.org/W2085961649","https://openalex.org/W2326034009","https://openalex.org/W2339025566","https://openalex.org/W2466677273","https://openalex.org/W2507558872","https://openalex.org/W2543926021","https://openalex.org/W2793325180","https://openalex.org/W2892103335"],"related_works":["https://openalex.org/W2027202866","https://openalex.org/W3149920197","https://openalex.org/W4293569346","https://openalex.org/W2397056152","https://openalex.org/W2949885877","https://openalex.org/W4252904065","https://openalex.org/W2734496778","https://openalex.org/W2494658963","https://openalex.org/W2129544565","https://openalex.org/W3017235236"],"abstract_inverted_index":{"In":[0,20],"this":[1],"paper,":[2],"we":[3,27,96],"consider":[4],"the":[5,23,38,42,47,51,63,69,103,107,117,126,130,155],"local":[6],"discontinuous":[7],"Galerkin":[8],"(LDG)":[9],"method":[10],"using":[11],"generalized":[12,146],"numerical":[13,48,93,118],"fluxes":[14,132],"for":[15,41,75,102],"linearized":[16],"Korteweg\u00e2\u0080\u0093de":[17],"Vries":[18],"equations.":[19],"particular,":[21],"since":[22],"dispersion":[24,52],"term":[25,44],"dominates,":[26],"are":[28,141,151],"able":[29],"to":[30,45,57,66,133,153],"choose":[31],"a":[32,59,99,134],"downwind-biased":[33],"flux":[34],"in":[35],"possession":[36],"of":[37,50,62,90,145],"anti-dissipation":[39],"property":[40],"convection":[43],"compensate":[46],"dissipation":[49],"term.":[53],"This":[54],"is":[55,121,125],"beneficial":[56],"obtain":[58],"lower":[60],"growth":[61],"error":[64,139],"and":[65,84,106],"accurately":[67],"capture":[68],"exact":[70],"solution":[71],"without":[72],"phase":[73],"errors":[74],"long":[76],"time":[77,114],"simulations,":[78],"when":[79],"compared":[80],"with":[81,129],"traditional":[82],"upwind":[83],"alternating":[85],"fluxes.":[86],"By":[87],"establishing":[88],"relations":[89],"three":[91],"different":[92],"viscosity":[94],"coefficients,":[95],"first":[97],"show":[98],"uniform":[100],"stability":[101],"auxiliary":[104],"variables":[105],"prime":[108],"variable":[109],"as":[110,112],"well":[111],"its":[113],"derivative.":[115],"Moreover,":[116],"initial":[119],"condition":[120],"suitably":[122],"chosen,":[123],"which":[124],"LDG":[127],"approximation":[128],"same":[131],"steady\u00e2\u0080\u0093state":[135],"equation.":[136],"Finally,":[137],"optimal":[138],"estimates":[140],"obtained":[142],"by":[143],"virtue":[144],"Gauss\u00e2\u0080\u0093Radau":[147],"projections.":[148],"Numerical":[149],"experiments":[150],"given":[152],"verify":[154],"theoretical":[156],"results.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}