{"id":"https://openalex.org/W4312050280","doi":"https://doi.org/10.1137/22m1470827","title":"A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg\u2013de Vries Equation","display_name":"A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg\u2013de Vries Equation","publication_year":2022,"publication_date":"2022-12-08","ids":{"openalex":"https://openalex.org/W4312050280","doi":"https://doi.org/10.1137/22m1470827"},"language":"en","primary_location":{"id":"doi:10.1137/22m1470827","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1470827","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/A5041162676","display_name":"Yanlai Chen","orcid":"https://orcid.org/0000-0002-7460-8313"},"institutions":[{"id":"https://openalex.org/I100633361","display_name":"University of Massachusetts Dartmouth","ror":"https://ror.org/00fzmm222","country_code":"US","type":"education","lineage":["https://openalex.org/I100633361"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yanlai Chen","raw_affiliation_strings":["Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA","institution_ids":["https://openalex.org/I100633361"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101734720","display_name":"Bo Dong","orcid":"https://orcid.org/0000-0003-4067-3763"},"institutions":[{"id":"https://openalex.org/I100633361","display_name":"University of Massachusetts Dartmouth","ror":"https://ror.org/00fzmm222","country_code":"US","type":"education","lineage":["https://openalex.org/I100633361"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Dong","raw_affiliation_strings":["Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA","institution_ids":["https://openalex.org/I100633361"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012035755","display_name":"Rebecca Pereira","orcid":null},"institutions":[{"id":"https://openalex.org/I100633361","display_name":"University of Massachusetts Dartmouth","ror":"https://ror.org/00fzmm222","country_code":"US","type":"education","lineage":["https://openalex.org/I100633361"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rebecca Pereira","raw_affiliation_strings":["Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747-2300 USA","institution_ids":["https://openalex.org/I100633361"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041162676"],"corresponding_institution_ids":["https://openalex.org/I100633361"],"apc_list":null,"apc_paid":null,"fwci":0.6084,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66296573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"6","first_page":"3078","last_page":"3098"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.8664222955703735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7873850464820862},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6726782321929932},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.616403341293335},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5335999131202698},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5261092782020569},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5221348404884338},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.5003132820129395},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49260932207107544},{"id":"https://openalex.org/keywords/energy-conservation","display_name":"Energy conservation","score":0.47133827209472656},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.423984557390213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33867260813713074},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2710801959037781},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24355125427246094},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08210715651512146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08068522810935974}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.8664222955703735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7873850464820862},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6726782321929932},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.616403341293335},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5335999131202698},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5261092782020569},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5221348404884338},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.5003132820129395},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49260932207107544},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.47133827209472656},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.423984557390213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33867260813713074},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2710801959037781},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24355125427246094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08210715651512146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08068522810935974},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1470827","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1470827","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":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G7445835402","display_name":null,"funder_award_id":"N00014-20-1-2849","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7805846986","display_name":null,"funder_award_id":"DMS-1818998","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320315739","display_name":"University of Massachusetts Dartmouth","ror":"https://ror.org/00fzmm222"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W398431032","https://openalex.org/W1549114415","https://openalex.org/W1975036160","https://openalex.org/W1975075848","https://openalex.org/W1979283178","https://openalex.org/W1984329364","https://openalex.org/W1988507032","https://openalex.org/W1993186872","https://openalex.org/W2001377050","https://openalex.org/W2007997432","https://openalex.org/W2008510006","https://openalex.org/W2009657287","https://openalex.org/W2014940857","https://openalex.org/W2017130050","https://openalex.org/W2027548498","https://openalex.org/W2040490308","https://openalex.org/W2044891421","https://openalex.org/W2046134068","https://openalex.org/W2068634975","https://openalex.org/W2069381275","https://openalex.org/W2079285567","https://openalex.org/W2085481725","https://openalex.org/W2118633257","https://openalex.org/W2130350269","https://openalex.org/W2158738915","https://openalex.org/W2161194605","https://openalex.org/W2172257354","https://openalex.org/W2339025566","https://openalex.org/W2415471936","https://openalex.org/W2466677273","https://openalex.org/W2913205632","https://openalex.org/W4248626225","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W2726528067","https://openalex.org/W2129573473","https://openalex.org/W169136837","https://openalex.org/W2380255313","https://openalex.org/W2952149072","https://openalex.org/W2154700905","https://openalex.org/W2138882090","https://openalex.org/W4366777355","https://openalex.org/W1488888950","https://openalex.org/W10626200"],"abstract_inverted_index":{".We":[0],"design,":[1],"analyze,":[2],"and":[3,43,113],"implement":[4],"a":[5,70,151,156],"new":[6,101],"conservative":[7],"discontinuous":[8],"Galerkin":[9],"(DG)":[10],"method":[11,31,63],"for":[12,73,158,163],"the":[13,20,33,36,40,60,74,83,97,109,116,119,124,128],"simulation":[14],"of":[15,29,39,51,78,111,118,127,138,166,171,173],"solitary":[16,79],"wave":[17],"solutions":[18,50],"to":[19,91,107],"generalized":[21],"Korteweg\u2013de":[22],"Vries":[23,168],"(KdV)":[24],"equation.":[25],"The":[26],"key":[27],"feature":[28],"our":[30,56,87],"is":[32,59,90],"conservation,":[34],"at":[35],"numerical":[37,98,120,134,161],"level,":[38],"mass,":[41],"energy,":[42],"Hamiltonian":[44,114],"that":[45,64],"are":[46,131,148],"conserved":[47],"by":[48,133,142],"exact":[49],"all":[52,66],"KdV":[53],"equations.":[54],"To":[55,81],"knowledge,":[57],"this":[58],"first":[61],"DG":[62],"conserves":[65],"these":[67],"three":[68],"quantities,":[69],"property":[71],"critical":[72],"accurate":[75],"long-time":[76],"evolution":[77],"waves.":[80],"achieve":[82],"desired":[84],"conservation":[85,110,125,140],"properties,":[86],"novel":[88],"idea":[89,137],"introduce":[92],"two":[93],"stabilization":[94],"parameters":[95],"in":[96,115],"fluxes":[99],"as":[100,155],"unknowns,":[102],"which":[103,130,147],"then":[104],"allow":[105],"us":[106],"enforce":[108],"energy":[112],"formulation":[117],"scheme.":[121],"We":[122],"prove":[123],"properties":[126,141],"scheme":[129],"corroborated":[132],"tests.":[135],"This":[136],"achieving":[139],"implicitly":[143],"defining":[144],"penalization":[145],"parameters,":[146],"traditionally":[149],"specified":[150],"priori,":[152],"can":[153],"serve":[154],"framework":[157],"designing":[159],"physics-preserving":[160],"methods":[162],"other":[164],"types":[165],"problems.KeywordsKorteweg\u2013de":[167],"equationdiscontinuous":[169],"Galerkinconservation":[170],"energyconservation":[172],"Hamiltonianimplicit":[174],"penalizationMSC":[175],"codes65M6065N30":[176]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}