{"id":"https://openalex.org/W1974854353","doi":"https://doi.org/10.1007/s10915-012-9648-x","title":"An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations","display_name":"An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations","publication_year":2012,"publication_date":"2012-10-05","ids":{"openalex":"https://openalex.org/W1974854353","doi":"https://doi.org/10.1007/s10915-012-9648-x","mag":"1974854353"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-012-9648-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-012-9648-x","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00741178","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001917610","display_name":"Olivier Bokanowski","orcid":"https://orcid.org/0000-0001-7108-2005"},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I201181511","display_name":"\u00c9cole Nationale Sup\u00e9rieure de Techniques Avanc\u00e9es","ror":"https://ror.org/0309cs235","country_code":"FR","type":"education","lineage":["https://openalex.org/I201181511","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Olivier Bokanowski","raw_affiliation_strings":["Lab. Jacques-Louis Lions, Univ. Pierre et Marie Curie, 75252, Paris Cedex 05, France","Projet Commands, ENSTA ParisTech, 828, Boulevard des Mar\u00e9chaux, 91762, Palaiseau Cedex, France","UFR de Math\u00e9matiques, Site Chevaleret, Univ. Paris-Diderot, 75205, Paris Cedex, France","Projet Commands, ENSTA ParisTech, Palaiseau Cedex, France","UFR de Math\u00e9matiques, Site Chevaleret, Univ. Paris-Diderot, Paris Cedex, France","Lab. Jacques-Louis Lions, Univ. Pierre et Marie Curie, Paris Cedex 05, France"],"affiliations":[{"raw_affiliation_string":"Lab. Jacques-Louis Lions, Univ. Pierre et Marie Curie, 75252, Paris Cedex 05, France","institution_ids":["https://openalex.org/I4210158291"]},{"raw_affiliation_string":"Projet Commands, ENSTA ParisTech, 828, Boulevard des Mar\u00e9chaux, 91762, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I201181511"]},{"raw_affiliation_string":"UFR de Math\u00e9matiques, Site Chevaleret, Univ. Paris-Diderot, 75205, Paris Cedex, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I169173203"]},{"raw_affiliation_string":"Projet Commands, ENSTA ParisTech, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I201181511"]},{"raw_affiliation_string":"UFR de Math\u00e9matiques, Site Chevaleret, Univ. Paris-Diderot, Paris Cedex, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I169173203"]},{"raw_affiliation_string":"Lab. Jacques-Louis Lions, Univ. Pierre et Marie Curie, Paris Cedex 05, France","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068763843","display_name":"Jochen Garcke","orcid":"https://orcid.org/0000-0002-8334-3695"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4210098248","display_name":"Fraunhofer Institute for Algorithms and Scientific Computing","ror":"https://ror.org/00trw9c49","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210098248","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jochen Garcke","raw_affiliation_strings":["Fraunhofer SCAI, Sankt Augustin, Germany","Institut f\u00fcr Numerische Simulation, Universtit\u00e4t Bonn, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer SCAI, Sankt Augustin, Germany","institution_ids":["https://openalex.org/I4210098248"]},{"raw_affiliation_string":"Institut f\u00fcr Numerische Simulation, Universtit\u00e4t Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028074195","display_name":"Michael Griebel","orcid":"https://orcid.org/0000-0002-3147-6680"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4210098248","display_name":"Fraunhofer Institute for Algorithms and Scientific Computing","ror":"https://ror.org/00trw9c49","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210098248","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Griebel","raw_affiliation_strings":["Fraunhofer SCAI, Sankt Augustin, Germany","Institut f\u00fcr Numerische Simulation, Universtit\u00e4t Bonn, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Fraunhofer SCAI, Sankt Augustin, Germany","institution_ids":["https://openalex.org/I4210098248"]},{"raw_affiliation_string":"Institut f\u00fcr Numerische Simulation, Universtit\u00e4t Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032294383","display_name":"Irene Klompmaker","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Irene Klompmaker","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001917610"],"corresponding_institution_ids":["https://openalex.org/I169173203","https://openalex.org/I201181511","https://openalex.org/I204730241","https://openalex.org/I4210158291"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":6.9951,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.97294948,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"55","issue":"3","first_page":"575","last_page":"605"},"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":0.998199999332428,"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":0.998199999332428,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976999759674072,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.7584347724914551},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.6455041170120239},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.6452677249908447},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5907005667686462},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5665902495384216},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5616241097450256},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5438611507415771},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5103806853294373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4990098476409912},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4973907768726349},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.46219828724861145},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41572025418281555},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2304704189300537},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08079981803894043}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7584347724914551},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.6455041170120239},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.6452677249908447},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5907005667686462},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5665902495384216},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5616241097450256},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5438611507415771},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5103806853294373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4990098476409912},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4973907768726349},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.46219828724861145},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41572025418281555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2304704189300537},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08079981803894043},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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":7,"locations":[{"id":"doi:10.1007/s10915-012-9648-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-012-9648-x","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.393.1708","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.393.1708","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/74/11/78/PDF/Bokanowski_Garcke_Griebel_Klompmaker_jsc.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.635.7273","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.635.7273","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal-ensta.archives-ouvertes.fr/docs/00/74/11/78/PDF/Bokanowski_Garcke_Griebel_Klompmaker_jsc.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.661.133","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.661.133","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dfg-spp1324.de/download/preprints/preprint122.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00741178v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00741178","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Scientific Computing, 2013, 55, pp. 575-605. &#x27E8;10.1007/s10915-012-9648-x&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:bonndoc.ulb.uni-bonn.de:20.500.11811/11937","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.11811/11937","pdf_url":null,"source":{"id":"https://openalex.org/S4306402493","display_name":"bonndoc (University of Bonn)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I135140700","host_organization_name":"University of Bonn","host_organization_lineage":["https://openalex.org/I135140700"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:preprint"},{"id":"pmh:oai:publica.fraunhofer.de:publica/232781","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/232781","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00741178v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00741178","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Scientific Computing, 2013, 55, pp. 575-605. &#x27E8;10.1007/s10915-012-9648-x&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W285505819","https://openalex.org/W587977125","https://openalex.org/W1487586009","https://openalex.org/W1489501223","https://openalex.org/W1522448884","https://openalex.org/W1970266193","https://openalex.org/W1975738182","https://openalex.org/W1983107435","https://openalex.org/W1991113069","https://openalex.org/W1993281803","https://openalex.org/W2015740317","https://openalex.org/W2021092589","https://openalex.org/W2027438381","https://openalex.org/W2039802576","https://openalex.org/W2054314432","https://openalex.org/W2056169118","https://openalex.org/W2058212189","https://openalex.org/W2059562419","https://openalex.org/W2064281833","https://openalex.org/W2076729694","https://openalex.org/W2116364955","https://openalex.org/W2142377262","https://openalex.org/W2326641952","https://openalex.org/W2394917699","https://openalex.org/W2403013574","https://openalex.org/W2407925552","https://openalex.org/W2481459718","https://openalex.org/W2519527018","https://openalex.org/W2615216662","https://openalex.org/W3147515309","https://openalex.org/W3161027129","https://openalex.org/W4255975175","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1983345526","https://openalex.org/W2076944689","https://openalex.org/W1594944678","https://openalex.org/W1977330547","https://openalex.org/W1487586009","https://openalex.org/W3102569876","https://openalex.org/W2971079383","https://openalex.org/W2061585064","https://openalex.org/W1997500459","https://openalex.org/W2061850819"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
