{"id":"https://openalex.org/W2037685118","doi":"https://doi.org/10.1137/100798715","title":"A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes","display_name":"A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2037685118","doi":"https://doi.org/10.1137/100798715","mag":"2037685118"},"language":"en","primary_location":{"id":"doi:10.1137/100798715","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100798715","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/inria-00455799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001315978","display_name":"Marco Picasso","orcid":"https://orcid.org/0000-0002-0069-5856"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Picasso","raw_affiliation_strings":["marco.picasso@epfl.ch#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"marco.picasso@epfl.ch#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046038516","display_name":"Fr\u00e9d\u00e9ric Alauzet","orcid":"https://orcid.org/0000-0002-8025-3862"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Alauzet","raw_affiliation_strings":["Frederic.alauzet@inria.fr and paul-louis.george@inria.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Frederic.alauzet@inria.fr and paul-louis.george@inria.fr#TAB#","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060827400","display_name":"Houman Borouchaki","orcid":"https://orcid.org/0000-0001-8912-3776"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Houman Borouchaki","raw_affiliation_strings":["houman.borouchaki@utt.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"houman.borouchaki@utt.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108394222","display_name":"Paul\u2010Louis George","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul-Louis George","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7329,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.89636384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"3","first_page":"1058","last_page":"1076"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9955999851226807,"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/polygon-mesh","display_name":"Polygon mesh","score":0.8390510082244873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.789281964302063},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.755684494972229},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7292067408561707},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5870417356491089},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5812534093856812},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5671293139457703},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.5195394158363342},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5157020688056946},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4634980857372284},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4545906186103821},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4340939223766327},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.43087148666381836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42928919196128845},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32145774364471436},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2747874855995178},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08456817269325256}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8390510082244873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.789281964302063},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.755684494972229},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7292067408561707},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5870417356491089},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5812534093856812},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5671293139457703},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.5195394158363342},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5157020688056946},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4634980857372284},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4545906186103821},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4340939223766327},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.43087148666381836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42928919196128845},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32145774364471436},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2747874855995178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08456817269325256},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/100798715","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100798715","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.413.4538","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.4538","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ann.jussieu.fr/~frey/papers/morphing/Picasso M., A numerical study of some Hessian recovery techniques on isotropic and anisotropic meshes.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:inria-00455799v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00455799","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":"[Research Report] RR-7202, INRIA. 2010, pp.25","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:infoscience.epfl.ch:169645","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/169645","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:169645","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/71777","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:HAL:inria-00455799v1","is_oa":true,"landing_page_url":"https://inria.hal.science/inria-00455799","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":"[Research Report] RR-7202, INRIA. 2010, pp.25","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1174798","https://openalex.org/W1928579664","https://openalex.org/W1968948586","https://openalex.org/W1976952637","https://openalex.org/W1979518155","https://openalex.org/W1979972914","https://openalex.org/W1982740015","https://openalex.org/W2003049157","https://openalex.org/W2018788206","https://openalex.org/W2036382499","https://openalex.org/W2039400225","https://openalex.org/W2042199582","https://openalex.org/W2044892973","https://openalex.org/W2046521061","https://openalex.org/W2053352684","https://openalex.org/W2057901099","https://openalex.org/W2065479689","https://openalex.org/W2069426867","https://openalex.org/W2086552710","https://openalex.org/W2091038863","https://openalex.org/W2095243069","https://openalex.org/W2095320818","https://openalex.org/W2101577814","https://openalex.org/W2110781362","https://openalex.org/W2123194316","https://openalex.org/W2127098673","https://openalex.org/W2129412583","https://openalex.org/W2131479138","https://openalex.org/W2155395549","https://openalex.org/W2162289385","https://openalex.org/W2193148151","https://openalex.org/W2199169705","https://openalex.org/W2267832109","https://openalex.org/W2909420370","https://openalex.org/W4233241017"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W1593744215","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W2083709218"],"abstract_inverted_index":{"Spaces":[0],"of":[1,38],"continuous":[2],"piecewise":[3],"linear":[4],"finite":[5],"elements":[6],"are":[7,18],"considered":[8],"to":[9,20,44],"solve":[10],"a":[11],"Poisson":[12],"problem,":[13],"and":[14,28,31,48],"several":[15],"numerical":[16],"methods":[17],"investigated":[19],"recover":[21],"second":[22],"derivatives.":[23],"Numerical":[24],"results":[25,40],"on":[26],"2D":[27],"3D":[29],"isotropic":[30],"anisotropic":[32],"meshes":[33],"indicate":[34],"that":[35,49],"the":[36,39,45],"quality":[37],"is":[41],"strongly":[42],"linked":[43],"mesh":[46],"topology":[47],"no":[50],"convergence":[51],"can":[52],"be":[53],"insured":[54],"in":[55],"general.":[56]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}