{"id":"https://openalex.org/W4401953170","doi":"https://doi.org/10.1090/mcom/4018","title":"A local discontinuous Galerkin method for the Novikov equation","display_name":"A local discontinuous Galerkin method for the Novikov equation","publication_year":2024,"publication_date":"2024-08-28","ids":{"openalex":"https://openalex.org/W4401953170","doi":"https://doi.org/10.1090/mcom/4018"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4018","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4018","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/A5100637099","display_name":"Qi Tao","orcid":"https://orcid.org/0000-0001-8549-1379"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qi Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025248530","display_name":"Xiang\u2010Ke Chang","orcid":"https://orcid.org/0000-0003-0056-8619"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiang-Ke Chang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089825319","display_name":"Yong Liu","orcid":"https://orcid.org/0000-0003-1385-0170"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yong Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047035333","display_name":"Chi\u2010Wang Shu","orcid":"https://orcid.org/0000-0001-7720-9564"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chi-Wang Shu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100637099"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.269,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53573857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"94","issue":"354","first_page":"1603","last_page":"1631"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994999766349792,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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/novikov-self-consistency-principle","display_name":"Novikov self-consistency principle","score":0.935640811920166},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6925969123840332},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49280741810798645},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42999985814094543},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42190349102020264},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.348460853099823},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27953895926475525},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23351168632507324},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.08412513136863708},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07451960444450378}],"concepts":[{"id":"https://openalex.org/C114170632","wikidata":"https://www.wikidata.org/wiki/Q2003641","display_name":"Novikov self-consistency principle","level":2,"score":0.935640811920166},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6925969123840332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49280741810798645},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42999985814094543},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42190349102020264},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.348460853099823},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27953895926475525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23351168632507324},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.08412513136863708},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07451960444450378}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4018","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4018","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/G1477633538","display_name":null,"funder_award_id":"DMS-2309249","funder_id":"https://openalex.org/F4320322847","funder_display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences"},{"id":"https://openalex.org/G3551301616","display_name":null,"funder_award_id":"DMS-2309249","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4628752813","display_name":null,"funder_award_id":"DMS-2309249","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/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322847","display_name":"Youth Innovation Promotion Association of the Chinese Academy of Sciences","ror":"https://ror.org/031141b54"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1973984954","https://openalex.org/W1976295558","https://openalex.org/W1986208932","https://openalex.org/W1998934494","https://openalex.org/W2010094764","https://openalex.org/W2012844428","https://openalex.org/W2012938047","https://openalex.org/W2015241123","https://openalex.org/W2019767773","https://openalex.org/W2022023445","https://openalex.org/W2024658602","https://openalex.org/W2026031976","https://openalex.org/W2045698591","https://openalex.org/W2046134068","https://openalex.org/W2052079008","https://openalex.org/W2052284980","https://openalex.org/W2064553589","https://openalex.org/W2065908448","https://openalex.org/W2066783603","https://openalex.org/W2069959378","https://openalex.org/W2084217855","https://openalex.org/W2085961649","https://openalex.org/W2090637157","https://openalex.org/W2122794051","https://openalex.org/W2153635930","https://openalex.org/W2189016775","https://openalex.org/W2268340786","https://openalex.org/W2320404402","https://openalex.org/W2328945630","https://openalex.org/W2468131123","https://openalex.org/W2507177345","https://openalex.org/W2749721619","https://openalex.org/W2775565734","https://openalex.org/W2905189568","https://openalex.org/W2946540522","https://openalex.org/W2963200540","https://openalex.org/W2963362066","https://openalex.org/W2964040987","https://openalex.org/W2964342860","https://openalex.org/W2995756203","https://openalex.org/W3184788886","https://openalex.org/W3207455116","https://openalex.org/W4221077469","https://openalex.org/W4221102314","https://openalex.org/W4226429135","https://openalex.org/W4246409132","https://openalex.org/W4255067042","https://openalex.org/W4286256627","https://openalex.org/W4376870041","https://openalex.org/W4382199631","https://openalex.org/W6687315095"],"related_works":["https://openalex.org/W2144706371","https://openalex.org/W2620684040","https://openalex.org/W4309010362","https://openalex.org/W3101663915","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2887215440","https://openalex.org/W1986323742","https://openalex.org/W2943697195","https://openalex.org/W2064065738"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5],"local":[6],"discontinuous":[7],"Galerkin":[8],"(LDG)":[9],"method":[10,83],"for":[11,63,84],"the":[12,28,31,56,60,76,81,86],"Novikov":[13,87],"equation":[14],"that":[15],"contains":[16],"cubic":[17],"nonlinear":[18],"high-order":[19],"derivatives.":[20],"Flux":[21],"correction":[22],"techniques":[23],"are":[24,71],"used":[25],"to":[26],"ensure":[27],"stability":[29,54],"of":[30,55,80],"numerical":[32],"scheme.":[33],"The":[34],"<inline-formula":[35],"content-type=\"math/mathml\">":[36],"<mml:math":[37],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[38],"alttext=\"upper":[39],"H":[40],"Superscript":[41],"1\">":[42],"<mml:semantics>":[43],"<mml:msup>":[44],"<mml:mi>H</mml:mi>":[45],"<mml:mn>1</mml:mn>":[46],"</mml:msup>":[47],"<mml:annotation":[48],"encoding=\"application/x-tex\">H^1</mml:annotation>":[49],"</mml:semantics>":[50],"</mml:math>":[51],"</inline-formula>":[52],"-norm":[53],"general":[57],"solution":[58],"and":[59,78],"error":[61],"estimate":[62],"smooth":[64],"solutions":[65],"without":[66],"using":[67],"any":[68],"priori":[69],"assumptions":[70],"presented.":[72],"Numerical":[73],"examples":[74],"demonstrate":[75],"accuracy":[77],"capability":[79],"LDG":[82],"solving":[85],"equation.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}