{"id":"https://openalex.org/W2088822153","doi":"https://doi.org/10.1137/110846397","title":"Pointwise a Posteriori Error Control for Discontinuous Galerkin Methods for Elliptic Problems","display_name":"Pointwise a Posteriori Error Control for Discontinuous Galerkin Methods for Elliptic Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2088822153","doi":"https://doi.org/10.1137/110846397","mag":"2088822153"},"language":"en","primary_location":{"id":"doi:10.1137/110846397","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110846397","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/A5070767719","display_name":"Alan Demlow","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan Demlow","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103928074","display_name":"Emmanuil H. Georgoulis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emmanuil H. Georgoulis","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070767719"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0988,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.86765868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"5","first_page":"2159","last_page":"2181"},"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":0.9983000159263611,"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/T10514","display_name":"Numerical methods in engineering","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/pointwise","display_name":"Pointwise","score":0.9226336479187012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.799443244934082},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7699670791625977},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7308138012886047},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.674075186252594},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.669855535030365},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6693916320800781},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.5895596742630005},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5856846570968628},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5141473412513733},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.4841530919075012},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47051042318344116},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3852585554122925},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19683539867401123}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.9226336479187012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.799443244934082},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7699670791625977},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7308138012886047},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.674075186252594},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.669855535030365},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6693916320800781},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.5895596742630005},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5856846570968628},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5141473412513733},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4841530919075012},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47051042318344116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3852585554122925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19683539867401123},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110846397","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110846397","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":40,"referenced_works":["https://openalex.org/W53208737","https://openalex.org/W1492326914","https://openalex.org/W1586623601","https://openalex.org/W1866311589","https://openalex.org/W1966768630","https://openalex.org/W1973664641","https://openalex.org/W1976565091","https://openalex.org/W1982199944","https://openalex.org/W1989665919","https://openalex.org/W1990275141","https://openalex.org/W1991960225","https://openalex.org/W1996672299","https://openalex.org/W1999035024","https://openalex.org/W2002086758","https://openalex.org/W2008303042","https://openalex.org/W2009985306","https://openalex.org/W2010610235","https://openalex.org/W2011913964","https://openalex.org/W2026757688","https://openalex.org/W2028338496","https://openalex.org/W2029725158","https://openalex.org/W2034290095","https://openalex.org/W2044627846","https://openalex.org/W2048108115","https://openalex.org/W2053695265","https://openalex.org/W2056470693","https://openalex.org/W2063974361","https://openalex.org/W2069048447","https://openalex.org/W2071036364","https://openalex.org/W2075653737","https://openalex.org/W2081210755","https://openalex.org/W2095507168","https://openalex.org/W2102295719","https://openalex.org/W2121031654","https://openalex.org/W2135855856","https://openalex.org/W2153299448","https://openalex.org/W2154063054","https://openalex.org/W2429258439","https://openalex.org/W2598764759","https://openalex.org/W3104006087"],"related_works":["https://openalex.org/W3162423863","https://openalex.org/W4361982689","https://openalex.org/W2613898712","https://openalex.org/W4327511427","https://openalex.org/W4385783739","https://openalex.org/W2394496373","https://openalex.org/W1748484423","https://openalex.org/W4323921997","https://openalex.org/W2008621392","https://openalex.org/W1991960225"],"abstract_inverted_index":{"An":[0],"a":[1,18,90],"posteriori":[2,91],"error":[3,9],"bound":[4],"for":[5,10,17,39,73],"the":[6,11,53,63,79,84,88],"maximum":[7],"(pointwise)":[8],"interior":[12],"penalty":[13],"discontinuous":[14],"Galerkin":[15],"method":[16],"standard":[19],"elliptic":[20],"model":[21],"problem":[22],"on":[23,52],"polyhedral":[24,46],"domains":[25,40],"is":[26,31,50],"presented.":[27,99],"The":[28,48],"computational":[29],"domain":[30],"not":[32],"required":[33],"to":[34],"be":[35],"Lipschitz,":[36],"thus":[37],"allowing":[38],"with":[41],"cracks":[42],"and":[43,59],"other":[44],"irregular":[45],"domains.":[47],"proof":[49],"based":[51],"direct":[54],"use":[55],"of":[56,69,87],"Green's":[57],"functions":[58],"varies":[60],"substantially":[61],"from":[62],"approach":[64],"used":[65],"in":[66,78],"previous":[67],"proofs":[68],"similar":[70],"$L_\\infty$":[71],"estimates":[72],"(continuous)":[74],"finite":[75],"element":[76],"methods":[77],"literature.":[80],"Numerical":[81],"experiments":[82],"indicating":[83],"good":[85],"behavior":[86],"resulting":[89],"bounds":[92],"within":[93],"an":[94],"adaptive":[95],"algorithm":[96],"are":[97],"also":[98]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}