{"id":"https://openalex.org/W2005448420","doi":"https://doi.org/10.1137/110856198","title":"On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations","display_name":"On the Convergence of Finite Element Methods for Hamilton--Jacobi--Bellman Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2005448420","doi":"https://doi.org/10.1137/110856198","mag":"2005448420"},"language":"en","primary_location":{"id":"doi:10.1137/110856198","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856198","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1111.5423","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Max Jensen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max Jensen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Iain Smears","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iain Smears","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2347,"has_fulltext":true,"cited_by_count":58,"citation_normalized_percentile":{"value":0.93993847,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"1","first_page":"137","last_page":"162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6736000180244446,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.6736000180244446,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.15929999947547913,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.03759999945759773,"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/finite-element-method","display_name":"Finite element method","score":0.70660001039505},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6459000110626221},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5073000192642212},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.48399999737739563},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4713999927043915},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4442000091075897},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.4235000014305115},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.39739999175071716},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.3707999885082245}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8628000020980835},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.70660001039505},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6459000110626221},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5073000192642212},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49779999256134033},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.48399999737739563},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4659999907016754},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.4235000014305115},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.3707999885082245},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.3529999852180481},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3456999957561493},{"id":"https://openalex.org/C4349628","wikidata":"https://www.wikidata.org/wiki/Q17027720","display_name":"hp-FEM","level":5,"score":0.33809998631477356},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.3005000054836273},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.2955000102519989},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.2732999920845032},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110856198","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110856198","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:arXiv.org:1111.5423","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1111.5423","pdf_url":"https://arxiv.org/pdf/1111.5423","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1111.5423","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1111.5423","pdf_url":"https://arxiv.org/pdf/1111.5423","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W61439753","https://openalex.org/W183349982","https://openalex.org/W1964377184","https://openalex.org/W1966068608","https://openalex.org/W1999545889","https://openalex.org/W2002182424","https://openalex.org/W2003116365","https://openalex.org/W2003316623","https://openalex.org/W2004745280","https://openalex.org/W2010634241","https://openalex.org/W2071557235","https://openalex.org/W2073691774","https://openalex.org/W2077883650","https://openalex.org/W2084358734","https://openalex.org/W2088299544","https://openalex.org/W2090061427","https://openalex.org/W2093895095","https://openalex.org/W2121031654","https://openalex.org/W2155369712","https://openalex.org/W2177195156","https://openalex.org/W2335457376","https://openalex.org/W2524112160"],"related_works":[],"abstract_inverted_index":{"We":[0,48],"study":[1],"the":[2,38,42,54,65],"convergence":[3,52,63],"of":[4,41,53,64],"monotone":[5],"$P1$":[6],"finite":[7],"element":[8],"methods":[9],"on":[10],"unstructured":[11],"meshes":[12],"for":[13],"fully":[14],"nonlinear":[15],"Hamilton--Jacobi--Bellman":[16],"equations":[17],"arising":[18],"from":[19],"stochastic":[20],"optimal":[21],"control":[22],"problems":[23],"with":[24],"possibly":[25],"degenerate,":[26],"isotropic":[27],"diffusions.":[28],"Using":[29],"elliptic":[30],"projection":[31],"operators":[32],"we":[33],"treat":[34],"discretizations":[35],"which":[36],"violate":[37],"consistency":[39],"conditions":[40],"framework":[43],"by":[44],"Barles":[45],"and":[46],"Souganidis.":[47],"obtain":[49],"strong":[50,61],"uniform":[51],"numerical":[55],"solutions":[56],"and,":[57],"under":[58],"nondegeneracy":[59],"assumptions,":[60],"$L^2$":[62],"gradients.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
