{"id":"https://openalex.org/W4407157584","doi":"https://doi.org/10.1090/mcom/4080","title":"Near and full quasi-optimality of finite element approximations of stationary second-order mean field games","display_name":"Near and full quasi-optimality of finite element approximations of stationary second-order mean field games","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4407157584","doi":"https://doi.org/10.1090/mcom/4080"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4080","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4080","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":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://durham-repository.worktribe.com/3798959/1/Accepted%20Journal%20Article","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022200676","display_name":"Yohance A. P. Osborne","orcid":"https://orcid.org/0000-0002-1313-2550"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yohance Osborne","raw_affiliation_strings":["Department of Mathematical Sciences, Durham University, Stockton Road, DH1 3LE Durham, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Durham University, Stockton Road, DH1 3LE Durham, United Kingdom","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003137738","display_name":"Iain Smears","orcid":"https://orcid.org/0000-0003-0005-4327"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Iain Smears","raw_affiliation_strings":["Department of Mathematics, University College London, Gower Street, WC1E 6BT London, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University College London, Gower Street, WC1E 6BT London, United Kingdom","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"358","first_page":"525","last_page":"555"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9614999890327454,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9614999890327454,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9297999739646912,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9297000169754028,"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/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.6944172382354736},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6066634654998779},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.544944703578949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48270249366760254},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.48175978660583496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40379804372787476},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35068953037261963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2521088719367981},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.14346441626548767},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08987265825271606}],"concepts":[{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.6944172382354736},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6066634654998779},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.544944703578949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48270249366760254},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.48175978660583496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40379804372787476},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35068953037261963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2521088719367981},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.14346441626548767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08987265825271606},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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":2,"locations":[{"id":"doi:10.1090/mcom/4080","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4080","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"},{"id":"pmh:oai:durham-repository.worktribe.com:3798959","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/3798959/1/Accepted%20Journal%20Article","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:durham-repository.worktribe.com:3798959","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/3798959/1/Accepted%20Journal%20Article","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3587405167","display_name":"Advanced Numerical Methods for Mean Field Games","funder_award_id":"EP/Y008758/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5216443068","display_name":null,"funder_award_id":"EP/Y008758/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8158814750","display_name":null,"funder_award_id":"EP/Y008758/1","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1866311589","https://openalex.org/W1929124830","https://openalex.org/W1981066502","https://openalex.org/W2003116365","https://openalex.org/W2005448420","https://openalex.org/W2009985306","https://openalex.org/W2011000015","https://openalex.org/W2028316825","https://openalex.org/W2035299975","https://openalex.org/W2038686546","https://openalex.org/W2057470999","https://openalex.org/W2077040879","https://openalex.org/W2088458423","https://openalex.org/W2095257746","https://openalex.org/W2155369712","https://openalex.org/W2168522485","https://openalex.org/W2246232185","https://openalex.org/W2497073464","https://openalex.org/W2744315941","https://openalex.org/W2963014769","https://openalex.org/W3157898245","https://openalex.org/W3204708751","https://openalex.org/W4205634890","https://openalex.org/W4223904870","https://openalex.org/W4294530603","https://openalex.org/W4311731041","https://openalex.org/W4382142027","https://openalex.org/W4390789582","https://openalex.org/W4390913432","https://openalex.org/W4403651580","https://openalex.org/W4407057483"],"related_works":["https://openalex.org/W2055836843","https://openalex.org/W2755775996","https://openalex.org/W3131818128","https://openalex.org/W2095941963","https://openalex.org/W2366062865","https://openalex.org/W2069701013","https://openalex.org/W2169158840","https://openalex.org/W1997375727","https://openalex.org/W2011633066","https://openalex.org/W4200392369"],"abstract_inverted_index":{"We":[0,88,108],"establish":[1],"a":[2],"priori":[3],"error":[4,50,62,97,117,155],"bounds":[5],"for":[6,103,149],"monotone":[7],"stabilized":[8],"finite":[9,66],"element":[10,67],"discretizations":[11],"of":[12,63,80,93,95,114,123,125,156],"stationary":[13],"second-order":[14],"mean":[15],"field":[16],"games":[17],"(MFG)":[18],"on":[19,45],"Lipschitz":[20],"polytopal":[21],"domains.":[22],"Under":[23],"suitable":[24],"hypotheses,":[25],"we":[26],"prove":[27],"that":[28,78,145],"the":[29,36,42,49,59,64,76,86,96,101,115,119,138,141,146,150,157,165],"approximation":[30,61,116,160],"is":[31,56,79,133,143],"asymptotically":[32],"nearly":[33],"quasi-optimal":[34],"in":[35,41,118,137,172],"H":[37,151,173],"1":[38,152,174],"H^1":[39,153,175],"-norm":[40,154],"sense":[43],"that,":[44],"sufficiently":[46],"fine":[47],"meshes,":[48],"between":[51],"exact":[52],"and":[53],"computed":[54],"solutions":[55,104],"bounded":[57],"by":[58],"best":[60],"corresponding":[65],"space,":[68],"plus":[69],"possibly":[70],"an":[71],"additional":[72],"term,":[73],"due":[74],"to":[75,85,100,134],"stabilization,":[77],"optimal":[81,91,162],"order":[82],"with":[83,98,105],"respect":[84,99],"mesh-size.":[87],"thereby":[89],"deduce":[90],"rates":[92],"convergence":[94,147],"mesh-size":[102],"sufficient":[106],"regularity.":[107],"further":[109,135],"show":[110],"full":[111],"asymptotic":[112],"quasi-optimality":[113],"more":[120],"restricted":[121],"case":[122,139],"sequences":[124],"strictly":[126],"acute":[127],"meshes.":[128],"Our":[129],"third":[130],"main":[131],"contribution":[132],"show,":[136],"where":[140],"domain":[142],"convex,":[144],"rate":[148],"value":[158],"function":[159,167],"remains":[161],"even":[163],"if":[164],"density":[166],"only":[168],"has":[169],"minimal":[170],"regularity":[171],".":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}