{"id":"https://openalex.org/W2099534371","doi":"https://doi.org/10.1137/100786046","title":"A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations","display_name":"A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2099534371","doi":"https://doi.org/10.1137/100786046","mag":"2099534371"},"language":"en","primary_location":{"id":"doi:10.1137/100786046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786046","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://hal.science/hal-00456837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062037573","display_name":"Yves Coudi\u00e8re","orcid":"https://orcid.org/0000-0003-2687-3232"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yves Coudi\u00e8re","raw_affiliation_strings":["Yves.Coudiere@univ-nantes.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yves.Coudiere@univ-nantes.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002731133","display_name":"Florence Hubert","orcid":"https://orcid.org/0000-0002-7553-9698"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Florence Hubert","raw_affiliation_strings":["florence.hubert@cmi.univ-mrs.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"florence.hubert@cmi.univ-mrs.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.565,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.98571071,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"33","issue":"4","first_page":"1739","last_page":"1764"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/duality","display_name":"Duality (order theory)","score":0.7946538329124451},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.756748378276825},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6942906975746155},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.6702829599380493},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.660952627658844},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6601924896240234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6293019652366638},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5833646655082703},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5089046955108643},{"id":"https://openalex.org/keywords/finite-volume-method-for-one-dimensional-steady-state-diffusion","display_name":"Finite volume method for one-dimensional steady state diffusion","score":0.4516458213329315},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4211200475692749},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30671602487564087},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22915443778038025},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.15796393156051636},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10779473185539246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10678842663764954},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.055268824100494385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.052246302366256714}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7946538329124451},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.756748378276825},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6942906975746155},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.6702829599380493},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.660952627658844},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6601924896240234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6293019652366638},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5833646655082703},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5089046955108643},{"id":"https://openalex.org/C85405225","wikidata":"https://www.wikidata.org/wiki/Q17013617","display_name":"Finite volume method for one-dimensional steady state diffusion","level":4,"score":0.4516458213329315},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4211200475692749},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30671602487564087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22915443778038025},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.15796393156051636},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10779473185539246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10678842663764954},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.055268824100494385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.052246302366256714},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100786046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100786046","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:10.1.1.406.3945","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.3945","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/45/68/37/PDF/ddfv3d.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00456837v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00456837","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":"SIAM Journal on Scientific Computing, 2011, 33 (4), pp.1739--1764. &#x27E8;10.1137/100786046&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00456837v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00456837","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":"SIAM Journal on Scientific Computing, 2011, 33 (4), pp.1739--1764. &#x27E8;10.1137/100786046&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5135727184","display_name":"Volumes Finis pour Situations Complexes","funder_award_id":"ANR-08-BLAN-0275","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1983124639","https://openalex.org/W2000450704","https://openalex.org/W2002757536","https://openalex.org/W2004302354","https://openalex.org/W2056923080","https://openalex.org/W2074387770","https://openalex.org/W2074742922","https://openalex.org/W2076014276","https://openalex.org/W2101501899","https://openalex.org/W2107487126","https://openalex.org/W2119306252","https://openalex.org/W2616300429","https://openalex.org/W2732922160","https://openalex.org/W4234074313"],"related_works":["https://openalex.org/W2163017860","https://openalex.org/W2034255721","https://openalex.org/W3042022377","https://openalex.org/W1999000186","https://openalex.org/W2086666789","https://openalex.org/W4206172935","https://openalex.org/W1997892295","https://openalex.org/W2095232916","https://openalex.org/W1557992730","https://openalex.org/W2338944697"],"abstract_inverted_index":{"Discrete":[0],"duality":[1],"finite":[2],"volume":[3],"(DDFV)":[4],"schemes":[5,29],"have":[6],"recently":[7],"been":[8],"developed":[9],"in":[10],"two":[11],"dimensions":[12],"to":[13,64],"approximate":[14],"nonlinear":[15],"diffusion":[16],"problems":[17],"on":[18],"general":[19],"meshes.":[20],"In":[21],"this":[22,35,56],"paper,":[23],"a":[24,45],"three-dimensional":[25],"extension":[26,36],"of":[27,34,55],"these":[28],"is":[30,37,58],"proposed.":[31],"The":[32,52],"construction":[33],"detailed":[38],"and":[39,49],"its":[40,66],"main":[41],"properties":[42],"are":[43,62],"proved:":[44],"priori":[46],"bounds,":[47],"well-posedness,":[48],"error":[50],"estimates.":[51],"practical":[53],"implementation":[54],"scheme":[57],"easy.":[59],"Numerical":[60],"experiments":[61],"presented":[63],"illustrate":[65],"good":[67],"behavior.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}
