{"id":"https://openalex.org/W118329571","doi":"https://doi.org/10.1137/130946873","title":"Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations","display_name":"Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W118329571","doi":"https://doi.org/10.1137/130946873","mag":"118329571"},"language":"en","primary_location":{"id":"doi:10.1137/130946873","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946873","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/A5021695845","display_name":"Waixiang Cao","orcid":"https://orcid.org/0000-0003-2434-7300"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Waixiang Cao","raw_affiliation_strings":["Sun Yat-Sen University"],"affiliations":[{"raw_affiliation_string":"Sun Yat-Sen University","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100406520","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-0531-9112"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053903143","display_name":"Qingsong Zou","orcid":"https://orcid.org/0000-0002-0710-7893"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qingsong Zou","raw_affiliation_strings":["Sun Yat-Sen University"],"affiliations":[{"raw_affiliation_string":"Sun Yat-Sen University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021695845"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3685,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.9816752,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"52","issue":"5","first_page":"2555","last_page":"2573"},"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994000196456909,"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/superconvergence","display_name":"Superconvergence","score":0.9929927587509155},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8501651883125305},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7643047571182251},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.71238112449646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.548085629940033},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.536882758140564},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4496331214904785},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.44530197978019714},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.42680540680885315},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.41742709279060364},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38465049862861633},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28640228509902954},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.28452104330062866},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.26047396659851074},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059540361166000366}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9929927587509155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8501651883125305},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7643047571182251},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.71238112449646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.548085629940033},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.536882758140564},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4496331214904785},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.44530197978019714},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.42680540680885315},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.41742709279060364},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38465049862861633},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28640228509902954},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.28452104330062866},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26047396659851074},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059540361166000366},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130946873","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130946873","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1971723751","https://openalex.org/W1982465309","https://openalex.org/W1982883068","https://openalex.org/W1991452709","https://openalex.org/W2012938047","https://openalex.org/W2023025416","https://openalex.org/W2029214106","https://openalex.org/W2033255950","https://openalex.org/W2044190355","https://openalex.org/W2049351608","https://openalex.org/W2070198016","https://openalex.org/W2082890708","https://openalex.org/W2085961649","https://openalex.org/W2098404380","https://openalex.org/W2116729868","https://openalex.org/W2129283513","https://openalex.org/W2148330860"],"related_works":["https://openalex.org/W2019032602","https://openalex.org/W4318305492","https://openalex.org/W4389778560","https://openalex.org/W3199641408","https://openalex.org/W2597229022","https://openalex.org/W2947552135","https://openalex.org/W2014920306","https://openalex.org/W2984453791","https://openalex.org/W1982175859","https://openalex.org/W2508014856"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,58],"study":[4],"superconvergence":[5,34],"properties":[6],"of":[7,36,64],"the":[8,30,37,41,46,61,65],"discontinuous":[9],"Galerkin":[10],"(DG)":[11],"method":[12],"for":[13,25,45],"one-dimensional":[14],"linear":[15],"hyperbolic":[16],"equations":[17],"when":[18],"upwind":[19],"fluxes":[20],"are":[21,83],"used.":[22],"We":[23],"prove,":[24],"any":[26],"polynomial":[27],"degree":[28],"$k$,":[29],"$2k+1$th":[31],"(or":[32],"$2k+1/2$th)":[33],"rate":[35,72],"DG":[38,66],"approximation":[39,63],"at":[40,74],"downwind":[42],"points":[43],"and":[44,52],"domain":[47],"average":[48],"under":[49],"quasi-uniform":[50],"meshes":[51],"some":[53],"suitable":[54],"initial":[55],"discretization.":[56],"Moreover,":[57],"prove":[59],"that":[60],"derivative":[62],"solution":[67],"is":[68],"superconvergent":[69],"with":[70],"a":[71],"$k+1$":[73],"all":[75],"interior":[76],"left":[77],"Radau":[78],"points.":[79],"All":[80],"theoretical":[81],"findings":[82],"confirmed":[84],"by":[85],"numerical":[86],"experiments.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}