{"id":"https://openalex.org/W2152605678","doi":"https://doi.org/10.1137/070685105","title":"Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems","display_name":"Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems","publication_year":2008,"publication_date":"2008-12-22","ids":{"openalex":"https://openalex.org/W2152605678","doi":"https://doi.org/10.1137/070685105","mag":"2152605678"},"language":"en","primary_location":{"id":"doi:10.1137/070685105","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070685105","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":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/103017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011409848","display_name":"Erik Burman","orcid":"https://orcid.org/0000-0003-4287-7241"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Burman","raw_affiliation_strings":["department of mathematics (United Kingdom)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"department of mathematics (United Kingdom)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036554395","display_name":"Benjamin Stamm","orcid":"https://orcid.org/0000-0003-3375-483X"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"B. Stamm","raw_affiliation_strings":["LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LJLL - Laboratoire Jacques-Louis Lions (Universit\u00e9 Pierre et Marie Curie, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0619,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.91728781,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"47","issue":"1","first_page":"508","last_page":"533"},"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":0.9975000023841858,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7483316659927368},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5967838168144226},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.555557906627655},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5552055835723877},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5287641286849976},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5282387137413025},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.525175929069519},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5198136568069458},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.50328129529953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45773816108703613},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45521068572998047},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42803704738616943},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3313882648944855},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.15441584587097168},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12741515040397644},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08791613578796387}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7483316659927368},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5967838168144226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.555557906627655},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5552055835723877},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5287641286849976},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5282387137413025},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.525175929069519},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5198136568069458},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.50328129529953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45773816108703613},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45521068572998047},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42803704738616943},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3313882648944855},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.15441584587097168},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12741515040397644},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08791613578796387},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/070685105","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070685105","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:CiteSeerX.psu:10.1.1.404.5982","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.404.5982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01090916v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01090916","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2009, 47 (1), pp.508-533. ⟨10.1137/070685105⟩","raw_type":"Journal articles"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1384716","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1384716/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM JOURNAL ON NUMERICAL ANALYSIS , 47  (1)   pp. 508-533.   (2008)      ","raw_type":"Article"},{"id":"pmh:oai:infoscience.epfl.ch:103017","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/103017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:publications.rwth-aachen.de:711440","is_oa":false,"landing_page_url":"http://publications.rwth-aachen.de/search?p=id:%22RWTH-2017-10801%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on numerical analysis 47(1), 508-533 (2009). doi:10.1137/070685105","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:103017","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/103017","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1572858226","https://openalex.org/W1585098889","https://openalex.org/W1601728065","https://openalex.org/W1968183962","https://openalex.org/W1971128923","https://openalex.org/W1972960967","https://openalex.org/W1977755392","https://openalex.org/W1979771104","https://openalex.org/W1986174760","https://openalex.org/W2009827206","https://openalex.org/W2012938047","https://openalex.org/W2017073125","https://openalex.org/W2029725158","https://openalex.org/W2031088298","https://openalex.org/W2041458840","https://openalex.org/W2073263351","https://openalex.org/W2079263908","https://openalex.org/W2135086547","https://openalex.org/W2149905008","https://openalex.org/W2158943855","https://openalex.org/W2415509676","https://openalex.org/W2477040106","https://openalex.org/W2592623476"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2366350639","https://openalex.org/W2087496541","https://openalex.org/W4295815745","https://openalex.org/W2953079798","https://openalex.org/W1969674427","https://openalex.org/W3092754077","https://openalex.org/W2982093746","https://openalex.org/W3043435143","https://openalex.org/W2158006240"],"abstract_inverted_index":{"We":[0,19,63],"consider":[1],"DG-methods":[2],"for":[3,57,87],"second":[4],"order":[5],"scalar":[6],"elliptic":[7],"problems":[8],"using":[9,68],"piecewise":[10,69],"affine":[11,70],"approximation":[12],"in":[13,48,83],"two":[14],"or":[15],"three":[16],"space":[17,78],"dimensions.":[18],"prove":[20,80],"that":[21,104],"both":[22,88],"the":[23,26,30,39,84,102,111],"symmetric":[24,90],"and":[25,61,91],"nonsymmetric":[27,92],"versions":[28],"of":[29,38,97,110],"DG-method":[31,67,93],"have":[32],"regular":[33,59],"system":[34],"matrices":[35],"without":[36,94],"penalization":[37],"interelement":[40],"solution":[41],"jumps":[42],"provided":[43],"boundary":[44],"conditions":[45],"are":[46],"imposed":[47],"a":[49,66,89],"certain":[50],"weak":[51],"manner.":[52],"Optimal":[53],"convergence":[54,82],"is":[55],"proved":[56],"sufficiently":[58],"meshes":[60],"data.":[62],"then":[64],"propose":[65],"functions":[71],"enriched":[72],"with":[73],"quadratic":[74],"bubbles.":[75],"Using":[76],"this":[77],"we":[79],"optimal":[81],"energy":[85],"norm":[86],"stabilization.":[95],"All":[96],"these":[98],"proposed":[99],"methods":[100],"share":[101],"feature":[103],"they":[105],"conserve":[106],"mass":[107],"locally":[108],"independent":[109],"penalty":[112],"parameter.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}