{"id":"https://openalex.org/W2056496693","doi":"https://doi.org/10.1137/05063831x","title":"Discontinuous Galerkin Methods for Friedrichs\u2019 Systems. Part II. Second\u2010order Elliptic PDEs","display_name":"Discontinuous Galerkin Methods for Friedrichs\u2019 Systems. Part II. Second\u2010order Elliptic PDEs","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2056496693","doi":"https://doi.org/10.1137/05063831x","mag":"2056496693"},"language":"en","primary_location":{"id":"doi:10.1137/05063831x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063831x","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/A5061539614","display_name":"Alexandre Ern","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Alexandre Ern","raw_affiliation_strings":["CERMICS, Ecole nationale des ponts et chauss\u00e9es, Champs sur Marne, 77455 Marne la Vall\u00e9e Cedex 2, France"],"affiliations":[{"raw_affiliation_string":"CERMICS, Ecole nationale des ponts et chauss\u00e9es, Champs sur Marne, 77455 Marne la Vall\u00e9e Cedex 2, France","institution_ids":["https://openalex.org/I142631665","https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045250454","display_name":"Jean\u2010Luc Guermond","orcid":"https://orcid.org/0000-0002-6974-6818"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210115485","display_name":"Laboratoire d'Informatique pour la M\u00e9canique et les Sciences de l'Ing\u00e9nieur","ror":"https://ror.org/01raq4x89","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210115485","https://openalex.org/I4210159245"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Jean\u2010Luc Guermond","raw_affiliation_strings":["LIMSI-CNRS, BP 133, 91403, Orsay, France","Dept. Math, Texas A&M, College Station, TX 77843-3368, USA (on leave from"],"affiliations":[{"raw_affiliation_string":"LIMSI-CNRS, BP 133, 91403, Orsay, France","institution_ids":["https://openalex.org/I4210115485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Dept. Math, Texas A&M, College Station, TX 77843-3368, USA (on leave from","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061539614"],"corresponding_institution_ids":["https://openalex.org/I142631665","https://openalex.org/I4210128309"],"apc_list":null,"apc_paid":null,"fwci":5.0934,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.95567955,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"44","issue":"6","first_page":"2363","last_page":"2388"},"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":0.9994000196456909,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9993000030517578,"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/mathematics","display_name":"Mathematics","score":0.7672759294509888},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7424342632293701},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6872351169586182},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46694910526275635},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.45891886949539185},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44138211011886597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43045711517333984},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4179355502128601},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3166927993297577},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08624458312988281}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7672759294509888},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7424342632293701},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6872351169586182},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46694910526275635},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.45891886949539185},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44138211011886597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43045711517333984},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4179355502128601},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3166927993297577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08624458312988281},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/05063831x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063831x","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:oaktrust.library.tamu.edu:1969.1/184236","is_oa":false,"landing_page_url":"https://hdl.handle.net/1969.1/184236","pdf_url":null,"source":{"id":"https://openalex.org/S4306400291","display_name":"OakTrust (Texas A&M University Libraries)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91045830","host_organization_name":"Texas A&M University","host_organization_lineage":["https://openalex.org/I91045830"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1480149586","https://openalex.org/W1964794014","https://openalex.org/W2012071009","https://openalex.org/W2012938047","https://openalex.org/W2017073125","https://openalex.org/W2029725158","https://openalex.org/W2069084681","https://openalex.org/W2079263908","https://openalex.org/W2082707061","https://openalex.org/W2130350269","https://openalex.org/W2150323068"],"related_works":["https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2196719869","https://openalex.org/W3097842552","https://openalex.org/W4298455509","https://openalex.org/W2952301147","https://openalex.org/W2076492300","https://openalex.org/W4372049316"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,23,64,71],"the":[3,52,73,80,88,96,100,110,133,143],"second":[4],"part":[5],"of":[6,15,25,47,132],"a":[7,12,30,45,129],"work":[8],"attempting":[9],"to":[10,43],"give":[11],"unified":[13],"analysis":[14],"discontinuous":[16,57,139],"Galerkin":[17,58,140],"methods.":[18],"The":[19,68],"setting":[20],"under":[21],"scrutiny":[22],"that":[24,72,75,103,113],"Friedrichs\u2019":[26],"systems":[27,63],"endowed":[28],"with":[29,137],"particular":[31],"$2":[32],"\\times":[33],"2$":[34],"structure":[35],"in":[36],"which":[37],"one":[38],"unknown":[39,74],"can":[40,76,83],"be":[41,77,85],"eliminated":[42,78,86],"yield":[44],"system":[46],"second\u2010order":[48],"elliptic\u2010like":[49],"PDEs":[50],"for":[51,60,123,142],"remaining":[53],"unknown.":[54],"A":[55],"general":[56],"method":[59],"approximating":[61],"such":[62],"proposed":[65],"and":[66,108,128],"analyzed.":[67],"key":[69],"feature":[70],"at":[79,87],"continuous":[81],"level":[82,90],"also":[84],"discrete":[89],"by":[91],"solving":[92],"local":[93],"problems.":[94],"All":[95],"design":[97],"constraints":[98],"on":[99,109],"boundary":[101,106],"operators":[102,112],"weakly":[104],"enforce":[105],"conditions":[107],"interface":[111,115],"penalize":[114],"jumps":[116],"are":[117,121,146],"fully":[118],"stated.":[119],"Examples":[120],"given":[122],"advection\u2010diffusion\u2010reaction,":[124],"linear":[125],"continuum":[126],"mechanics,":[127],"simplified":[130],"version":[131],"magnetohydrodynamics":[134],"equations.":[135],"Comparisons":[136],"well\u2010known":[138],"approximations":[141],"Poisson":[144],"equation":[145],"presented.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}