{"id":"https://openalex.org/W2065429647","doi":"https://doi.org/10.1090/s0025-5718-04-01651-5","title":"Failure of the discrete maximum principle for an elliptic finite element problem","display_name":"Failure of the discrete maximum principle for an elliptic finite element problem","publication_year":2004,"publication_date":"2004-03-23","ids":{"openalex":"https://openalex.org/W2065429647","doi":"https://doi.org/10.1090/s0025-5718-04-01651-5","mag":"2065429647"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-04-01651-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01651-5","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01651-5/S0025-5718-04-01651-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01651-5/S0025-5718-04-01651-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016752483","display_name":"Andrei Dr\u0103g\u0103nescu","orcid":"https://orcid.org/0009-0001-1425-8374"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrei Dr\u0103g\u0103nescu","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, Illinois 60637"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102273369","display_name":"Todd F. Dupont","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd Dupont","raw_affiliation_strings":["Department of Computer Science, University of Chicago, Chicago, Illinois 60637","Department of Computer Science, University of Chicago, Chicago, Illinois, 60637#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Department of Computer Science, University of Chicago, Chicago, Illinois, 60637#TAB#","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068215959","display_name":"L. Ridgway Scott","orcid":"https://orcid.org/0000-0002-7885-7106"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Scott","raw_affiliation_strings":["Department of Mathematics, University of Chicago, Chicago, Illinois 60637"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago, Chicago, Illinois 60637","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016752483"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":5.0068,"has_fulltext":true,"cited_by_count":104,"citation_normalized_percentile":{"value":0.95026148,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"74","issue":"249","first_page":"1","last_page":"23"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8595614433288574},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7031453251838684},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.4330233633518219},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.41990533471107483},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.41583192348480225},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.413673996925354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36914584040641785},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25536996126174927},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08607307076454163},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.05018746852874756}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8595614433288574},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7031453251838684},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.4330233633518219},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.41990533471107483},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.41583192348480225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.413673996925354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36914584040641785},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25536996126174927},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08607307076454163},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.05018746852874756},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-04-01651-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01651-5","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01651-5/S0025-5718-04-01651-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.3537","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.3537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2005-74-249/S0025-5718-04-01651-5/S0025-5718-04-01651-5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-04-01651-5","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01651-5","pdf_url":"https://www.ams.org/mcom/2005-74-249/S0025-5718-04-01651-5/S0025-5718-04-01651-5.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1172940792","display_name":null,"funder_award_id":"DMR-0213745","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4738448618","display_name":null,"funder_award_id":"DMR-0213745","funder_id":"https://openalex.org/F4320337367","funder_display_name":"Division of Materials Research"},{"id":"https://openalex.org/G4897846068","display_name":"Materials Research Science and Engineering Center","funder_award_id":"0213745","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309626","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28"},{"id":"https://openalex.org/F4320333422","display_name":"Materials Research Science and Engineering Center, Harvard University","ror":null},{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065429647.pdf","grobid_xml":"https://content.openalex.org/works/W2065429647.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W41827812","https://openalex.org/W1492326914","https://openalex.org/W1533902011","https://openalex.org/W2003116365","https://openalex.org/W2034029678","https://openalex.org/W2038914044","https://openalex.org/W2044355921","https://openalex.org/W2052084709","https://openalex.org/W2058639681","https://openalex.org/W2065279412","https://openalex.org/W2140505128","https://openalex.org/W2321310861","https://openalex.org/W3035235874","https://openalex.org/W4210574324","https://openalex.org/W4234694874","https://openalex.org/W6823358264"],"related_works":["https://openalex.org/W2021654023","https://openalex.org/W4254088695","https://openalex.org/W2367880982","https://openalex.org/W1964128728","https://openalex.org/W2360811052","https://openalex.org/W2112506890","https://openalex.org/W2077845843","https://openalex.org/W206336013","https://openalex.org/W2502579552","https://openalex.org/W128188719"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"a":[3,14,25],"long-standing":[4],"question":[5,75],"of":[6,29,52,110,131],"whether":[7,38],"certain":[8],"mesh":[9],"restrictions":[10],"are":[11,130],"required":[12],"for":[13,19,45,76],"maximum":[15],"condition":[16],"to":[17,36,116],"hold":[18],"the":[20,39,77,85,100,108],"discrete":[21,40,126],"equations":[22],"arising":[23],"from":[24],"finite":[26],"element":[27],"approximation":[28,51],"an":[30],"elliptic":[31],"problem.":[32],"This":[33],"is":[34,43,102,114],"related":[35],"knowing":[37],"Green\u2019s":[41,127],"function":[42],"positive":[44],"triangular":[46],"meshes":[47],"allowing":[48],"sufficiently":[49],"good":[50],"<inline-formula":[53],"content-type=\"math/mathml\">":[54],"<mml:math":[55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[56],"alttext=\"upper":[57],"H":[58],"Superscript":[59],"1\">":[60],"<mml:semantics>":[61],"<mml:msup>":[62],"<mml:mi>H</mml:mi>":[63],"<mml:mn>1</mml:mn>":[64],"</mml:msup>":[65],"<mml:annotation":[66],"encoding=\"application/x-tex\">H^1</mml:annotation>":[67],"</mml:semantics>":[68],"</mml:math>":[69],"</inline-formula>":[70],"functions.":[71],"We":[72,92],"study":[73],"this":[74],"Poisson":[78],"problem":[79],"in":[80,98],"two":[81],"dimensions":[82],"discretized":[83],"via":[84],"Galerkin":[86],"method":[87],"with":[88],"continuous":[89],"piecewise":[90],"linears.":[91],"give":[93],"examples":[94],"which":[95],"show":[96],"that":[97,129],"general":[99],"answer":[101],"negative,":[103],"and":[104],"furthermore":[105],"we":[106],"extend":[107],"number":[109],"cases":[111],"where":[112],"it":[113],"known":[115],"be":[117],"positive.":[118],"Our":[119],"techniques":[120],"utilize":[121],"some":[122],"new":[123],"results":[124],"about":[125],"functions":[128],"independent":[132],"interest.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}