{"id":"https://openalex.org/W2130350269","doi":"https://doi.org/10.1137/s0036142901384162","title":"Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems","display_name":"Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2130350269","doi":"https://doi.org/10.1137/s0036142901384162","mag":"2130350269"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901384162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384162","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/A5067734351","display_name":"Douglas N. Arnold","orcid":"https://orcid.org/0000-0002-0805-7672"},"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":"Douglas N. Arnold","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/A5073696154","display_name":"Franco Brezzi","orcid":"https://orcid.org/0000-0003-4715-5475"},"institutions":[{"id":"https://openalex.org/I197604219","display_name":"National Academies of Sciences, Engineering, and Medicine","ror":"https://ror.org/02eq2w707","country_code":"US","type":"government","lineage":["https://openalex.org/I197604219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Franco Brezzi","raw_affiliation_strings":["National Res. Council, Italy"],"affiliations":[{"raw_affiliation_string":"National Res. Council, Italy","institution_ids":["https://openalex.org/I197604219"]}]},{"author_position":"middle","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":false,"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":"last","author":{"id":"https://openalex.org/A5056811351","display_name":"L. D. Marini","orcid":"https://orcid.org/0000-0002-9224-1367"},"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":false,"raw_author_name":"L. Donatella Marini","raw_affiliation_strings":["University of\u00a0Minnesota"],"affiliations":[{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5067734351"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":77.6282,"has_fulltext":false,"cited_by_count":3232,"citation_normalized_percentile":{"value":0.99992531,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"39","issue":"5","first_page":"1749","last_page":"1779"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.9171011447906494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7500685453414917},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6015716195106506},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.49016842246055603},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4825662672519684},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46483537554740906},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4187103807926178},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.38928669691085815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37995991110801697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14293444156646729},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05702406167984009}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.9171011447906494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7500685453414917},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6015716195106506},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.49016842246055603},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4825662672519684},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46483537554740906},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4187103807926178},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.38928669691085815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37995991110801697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14293444156646729},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05702406167984009},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142901384162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384162","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:11299/3539","is_oa":false,"landing_page_url":"http://purl.umn.edu/3539","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:10.1.1.185.164","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://umn.edu/%7Earnold/papers/dgerr.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W6303485","https://openalex.org/W49087508","https://openalex.org/W49566120","https://openalex.org/W70071832","https://openalex.org/W180136160","https://openalex.org/W201696685","https://openalex.org/W222841820","https://openalex.org/W1494596325","https://openalex.org/W1494944027","https://openalex.org/W1507767947","https://openalex.org/W1516155022","https://openalex.org/W1534562927","https://openalex.org/W1545082185","https://openalex.org/W1547166419","https://openalex.org/W1585098889","https://openalex.org/W1588534530","https://openalex.org/W1600997507","https://openalex.org/W1770074644","https://openalex.org/W1852082788","https://openalex.org/W1947782577","https://openalex.org/W1973312823","https://openalex.org/W1974535188","https://openalex.org/W1982465309","https://openalex.org/W1982883068","https://openalex.org/W1985570191","https://openalex.org/W1986174760","https://openalex.org/W1987826592","https://openalex.org/W1989331860","https://openalex.org/W1992066344","https://openalex.org/W1993311738","https://openalex.org/W1993923624","https://openalex.org/W1996858170","https://openalex.org/W2006669401","https://openalex.org/W2010517168","https://openalex.org/W2012938047","https://openalex.org/W2017073125","https://openalex.org/W2026947527","https://openalex.org/W2028928494","https://openalex.org/W2029017626","https://openalex.org/W2029725158","https://openalex.org/W2031088298","https://openalex.org/W2031693957","https://openalex.org/W2037332128","https://openalex.org/W2040011362","https://openalex.org/W2041458840","https://openalex.org/W2041523977","https://openalex.org/W2059694340","https://openalex.org/W2062618977","https://openalex.org/W2062839853","https://openalex.org/W2063086331","https://openalex.org/W2065908448","https://openalex.org/W2066706262","https://openalex.org/W2067962368","https://openalex.org/W2069036386","https://openalex.org/W2074305223","https://openalex.org/W2079263908","https://openalex.org/W2079423956","https://openalex.org/W2082741499","https://openalex.org/W2085961649","https://openalex.org/W2090116345","https://openalex.org/W2116469836","https://openalex.org/W2121989547","https://openalex.org/W2154700905","https://openalex.org/W2158574387","https://openalex.org/W2479820417","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W1965109456","https://openalex.org/W2244225468","https://openalex.org/W2964178063","https://openalex.org/W968924973","https://openalex.org/W2435162739","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"provide":[2],"a":[3,9],"framework":[4],"for":[5,15,21,42],"the":[6,22,29,38,43],"analysis":[7],"of":[8,12,26,28,46],"large":[10],"class":[11],"discontinuous":[13,30],"methods":[14,32],"second-order":[16],"elliptic":[17,47],"problems.":[18,48],"It":[19],"allows":[20],"understanding":[23],"and":[24],"comparison":[25],"most":[27],"Galerkin":[31],"that":[33],"have":[34],"been":[35],"proposed":[36],"over":[37],"past":[39],"three":[40],"decades":[41],"numerical":[44],"treatment":[45]},"counts_by_year":[{"year":2026,"cited_by_count":28},{"year":2025,"cited_by_count":100},{"year":2024,"cited_by_count":127},{"year":2023,"cited_by_count":135},{"year":2022,"cited_by_count":108},{"year":2021,"cited_by_count":174},{"year":2020,"cited_by_count":204},{"year":2019,"cited_by_count":190},{"year":2018,"cited_by_count":181},{"year":2017,"cited_by_count":190},{"year":2016,"cited_by_count":158},{"year":2015,"cited_by_count":177},{"year":2014,"cited_by_count":218},{"year":2013,"cited_by_count":166},{"year":2012,"cited_by_count":176}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}