{"id":"https://openalex.org/W2069036386","doi":"https://doi.org/10.1137/s0036142900371544","title":"Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids","display_name":"Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2069036386","doi":"https://doi.org/10.1137/s0036142900371544","mag":"2069036386"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900371544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900371544","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/A5091258269","display_name":"Bernardo Cockburn","orcid":"https://orcid.org/0000-0001-6085-3441"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bernardo Cockburn","raw_affiliation_strings":["University of\u00a0Minnesota"],"affiliations":[{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074603830","display_name":"Guido Kanschat","orcid":"https://orcid.org/0000-0003-1687-7328"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Guido Kanschat","raw_affiliation_strings":["Heidelberg University"],"affiliations":[{"raw_affiliation_string":"Heidelberg University","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014923839","display_name":"Ilaria Perugia","orcid":"https://orcid.org/0000-0003-1368-2883"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ilaria Perugia","raw_affiliation_strings":["University of Pavia"],"affiliations":[{"raw_affiliation_string":"University of Pavia","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000032948","display_name":"Dominik Sch\u00f6tzau","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dominik Sch\u00f6tzau","raw_affiliation_strings":["University of Minnesota Twin Cities"],"affiliations":[{"raw_affiliation_string":"University of Minnesota Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091258269"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":12.7362,"has_fulltext":true,"cited_by_count":344,"citation_normalized_percentile":{"value":0.99098114,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"39","issue":"1","first_page":"264","last_page":"285"},"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":1.0,"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":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9983999729156494,"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/superconvergence","display_name":"Superconvergence","score":0.9628257751464844},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8392715454101562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8127291798591614},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6415583491325378},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.5995323061943054},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5844782590866089},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5316748023033142},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.5177634954452515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42980796098709106},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42779096961021423},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38284581899642944},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3092324733734131},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30223721265792847},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20887491106987},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12845411896705627},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07570338249206543}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.9628257751464844},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8392715454101562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8127291798591614},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6415583491325378},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5995323061943054},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5844782590866089},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5316748023033142},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.5177634954452515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42980796098709106},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42779096961021423},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38284581899642944},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3092324733734131},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30223721265792847},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20887491106987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12845411896705627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07570338249206543},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142900371544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900371544","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"},{"id":"pmh:oai:conservancy.umn.edu:11299/3441","is_oa":false,"landing_page_url":"http://purl.umn.edu/3441","pdf_url":null,"source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.2791","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.2791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.msi.umn.edu/general/Reports/rptfiles/UMSI2000-71/UMSI_2000-71.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W6303485","https://openalex.org/W202835528","https://openalex.org/W1987826592","https://openalex.org/W2012938047","https://openalex.org/W2041458840","https://openalex.org/W2041523977","https://openalex.org/W2046914952","https://openalex.org/W2063164826"],"related_works":["https://openalex.org/W2048180566","https://openalex.org/W3123659167","https://openalex.org/W3092754077","https://openalex.org/W1999579808","https://openalex.org/W2022721275","https://openalex.org/W2613065869","https://openalex.org/W2140272862","https://openalex.org/W3209842072","https://openalex.org/W2918697861","https://openalex.org/W2069036386"],"abstract_inverted_index":{"In":[0],"this":[1,63],"paper,":[2],"we":[3],"present":[4,79],"a":[5,16,25,80],"superconvergence":[6],"result":[7],"for":[8,15,29,60],"the":[9,31,34,37,40,69,87],"local":[10],"discontinuous":[11],"Galerkin":[12],"(LDG)":[13],"method":[14,66],"model":[17],"elliptic":[18],"problem":[19],"on":[20],"Cartesian":[21],"grids.":[22],"We":[23,78],"identify":[24],"special":[26,64],"numerical":[27,83],"flux":[28],"which":[30,85],"L2-norm":[32,38],"of":[33,39,43,53,71,73,82,89],"gradient":[35],"and":[36,46,75],"potential":[41],"are":[42,58],"orders":[44,70],"k+1/2":[45],"k+1,":[47],"respectively,":[48],"when":[49],"tensor":[50],"product":[51],"polynomials":[52],"degree":[54],"at":[55],"most":[56],"k":[57,74],"used;":[59],"arbitrary":[61],"meshes,":[62],"LDG":[65],"gives":[67],"only":[68],"convergence":[72],"k+1/2,":[76],"respectively.":[77],"series":[81],"examples":[84],"establish":[86],"sharpness":[88],"our":[90],"theoretical":[91],"results.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":18}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
