{"id":"https://openalex.org/W4406780334","doi":"https://doi.org/10.1090/mcom/4040","title":"A class of discontinuous Galerkin methods for nonlinear variational problems","display_name":"A class of discontinuous Galerkin methods for nonlinear variational problems","publication_year":2025,"publication_date":"2025-01-23","ids":{"openalex":"https://openalex.org/W4406780334","doi":"https://doi.org/10.1090/mcom/4040"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4040","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4040","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026060713","display_name":"Georgios Grekas","orcid":"https://orcid.org/0000-0002-0267-0150"},"institutions":[{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"G. Grekas","raw_affiliation_strings":["Institute of Applied & Computational Mathematics, Foundation for Research & Technology-Hellas; and Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied & Computational Mathematics, Foundation for Research & Technology-Hellas; and Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I8901234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077849399","display_name":"Konstantinos Koumatos","orcid":"https://orcid.org/0000-0002-9760-6839"},"institutions":[{"id":"https://openalex.org/I162608824","display_name":"University of Sussex","ror":"https://ror.org/00ayhx656","country_code":"GB","type":"education","lineage":["https://openalex.org/I162608824"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"K. Koumatos","raw_affiliation_strings":["Department of Mathematics, University of Sussex"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sussex","institution_ids":["https://openalex.org/I162608824"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112742097","display_name":"C. Makridakis","orcid":null},"institutions":[{"id":"https://openalex.org/I8901234","display_name":"Foundation for Research and Technology Hellas","ror":"https://ror.org/052rphn09","country_code":"GR","type":"facility","lineage":["https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"C. Makridakis","raw_affiliation_strings":["Institute of Applied & Computational Mathematics, Foundation for Research & Technology-Hellas; and Department of Mathematics, University of Sussex; and Department of Mathematics and Applied Mathematics, University of Crete"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied & Computational Mathematics, Foundation for Research & Technology-Hellas; and Department of Mathematics, University of Sussex; and Department of Mathematics and Applied Mathematics, University of Crete","institution_ids":["https://openalex.org/I8901234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083131603","display_name":"Andreas Vikelis","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"A. Vikelis","raw_affiliation_strings":["Faculty of Mathematics, University of Vienna"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6189,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56338745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"94","issue":"355","first_page":"2221","last_page":"2250"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8872063159942627},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7046315670013428},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6915085315704346},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6470426321029663},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.559986412525177},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.539096474647522},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4265936017036438},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3477715849876404},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.221140056848526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.047813624143600464},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.039890557527542114}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8872063159942627},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7046315670013428},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6915085315704346},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6470426321029663},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.559986412525177},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.539096474647522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4265936017036438},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3477715849876404},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.221140056848526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.047813624143600464},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.039890557527542114},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4040","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4040","pdf_url":null,"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2764986547","display_name":null,"funder_award_id":"Vannevar Bush Postdoctoral Fellowship. N00014-19-1-2623","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2955857586","display_name":null,"funder_award_id":"EP/X038998/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5218181193","display_name":"Elasticity: on the interface between statics and dynamics","funder_award_id":"EP/X038998/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G628593090","display_name":null,"funder_award_id":"Vannevar Bush Postdoctoral Fellowship. N00014-19-1-2623","funder_id":"https://openalex.org/F4320333578","funder_display_name":"Office of the Under Secretary of Defense"},{"id":"https://openalex.org/G7192002971","display_name":null,"funder_award_id":"EP/X038998/1","funder_id":"https://openalex.org/F4320333578","funder_display_name":"Office of the Under Secretary of Defense"}],"funders":[{"id":"https://openalex.org/F4320333578","display_name":"Office of the Under Secretary of Defense","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1480714962","https://openalex.org/W1972109318","https://openalex.org/W1991960225","https://openalex.org/W1996885477","https://openalex.org/W2012701400","https://openalex.org/W2029725158","https://openalex.org/W2042816276","https://openalex.org/W2061125163","https://openalex.org/W2071928229","https://openalex.org/W2081513515","https://openalex.org/W2136256106","https://openalex.org/W2137985153","https://openalex.org/W2155061016","https://openalex.org/W2182274314","https://openalex.org/W2251490743","https://openalex.org/W2964065979","https://openalex.org/W2992438785","https://openalex.org/W3097492579","https://openalex.org/W3115740056","https://openalex.org/W3185147866","https://openalex.org/W3202278567","https://openalex.org/W3204708751","https://openalex.org/W4232597038","https://openalex.org/W4252855540"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1965109456","https://openalex.org/W2435162739","https://openalex.org/W2244225468","https://openalex.org/W4235910846","https://openalex.org/W2162026849","https://openalex.org/W3118756358","https://openalex.org/W2394687667","https://openalex.org/W2887215440"],"abstract_inverted_index":{"In":[0,72],"the":[1,23,38,46,50,57,66,69,79,82,85,107,117],"context":[2],"of":[3,10,45,60,68,84,111,119],"discontinuous":[4],"Galerkin":[5],"methods,":[6],"we":[7,32,74,95],"study":[8],"approximations":[9],"nonlinear":[11],"variational":[12],"problems.":[13],"We":[14,114],"propose":[15],"element-wise":[16],"nonconforming":[17],"finite":[18],"element":[19],"methods":[20,121],"to":[21,42,54],"discretize":[22],"continuous":[24,47,86],"minimisation":[25],"problem.":[26],"Using":[27],"\u0393":[28],"\\Gamma":[29],"-convergence":[30],"arguments":[31],"show":[33,96],"that":[34],"for":[35,106],"convex":[36],"energies":[37],"discrete":[39,70,108],"minimisers":[40],"converge":[41],"a":[43],"minimiser":[44],"problem":[48,88],"as":[49],"mesh":[51],"parameter":[52],"tends":[53],"zero,":[55],"under":[56],"additional":[58],"contribution":[59],"appropriately":[61],"defined":[62],"penalty":[63],"terms":[64],"at":[65],"level":[67],"energies.":[71],"addition,":[73],"provide":[75],"error":[76,104],"analysis":[77],"in":[78],"case":[80],"where":[81],"solution":[83],"minimization":[87],"is":[89],"smooth":[90],"enough.":[91],"Under":[92],"appropriate":[93],"assumptions":[94],"local":[97],"existence,":[98],"uniqueness":[99],"and":[100],"corresponding":[101],"optimal":[102],"order":[103],"estimates":[105],"Euler-Lagrange":[109],"equations":[110],"our":[112,120],"scheme.":[113],"finally":[115],"substantiate":[116],"feasibility":[118],"by":[122],"numerical":[123],"examples.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
