{"id":"https://openalex.org/W2036663341","doi":"https://doi.org/10.1137/060655031","title":"A Discrete Duality Finite Volume Approach to Hodge Decomposition and div\u2010curl Problems on Almost Arbitrary Two\u2010Dimensional Meshes","display_name":"A Discrete Duality Finite Volume Approach to Hodge Decomposition and div\u2010curl Problems on Almost Arbitrary Two\u2010Dimensional Meshes","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2036663341","doi":"https://doi.org/10.1137/060655031","mag":"2036663341"},"language":"en","primary_location":{"id":"doi:10.1137/060655031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060655031","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071878696","display_name":"Sarah Delcourte","orcid":"https://orcid.org/0000-0003-1904-177X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sarah Delcourte","raw_affiliation_strings":["LMPE - Laboratoire de Mod\u00e9lisation Physique et de l'Enrichissement (France)"],"affiliations":[{"raw_affiliation_string":"LMPE - Laboratoire de Mod\u00e9lisation Physique et de l'Enrichissement (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072315074","display_name":"Komla Domelevo","orcid":"https://orcid.org/0000-0002-6634-7563"},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Komla Domelevo","raw_affiliation_strings":["IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)"],"affiliations":[{"raw_affiliation_string":"IMT - Institut de Math\u00e9matiques de Toulouse UMR5219 (UPS IMT, F-31062 Toulouse Cedex 9, \r\nINSA Toulouse, F-31077 Toulouse,\r\nFrance UT1, F-31042 Toulouse, \r\nFrance UT2, F-31058 Toulouse,\r\n\r\nT\u00e9l\u00e9phone : 05.61.55.67.90 - France)","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555","https://openalex.org/I196454796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064222048","display_name":"Pascal Omn\u00e8s","orcid":"https://orcid.org/0000-0002-0480-7085"},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210127723","display_name":"Direction des Energies","ror":"https://ror.org/03cwzta72","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I4210127723"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pascal Omnes","raw_affiliation_strings":["LAGA - Laboratoire Analyse, G\u00e9om\u00e9trie et Applications (Institut Galil\u00e9e, Universit\u00e9 Paris 13, 99 avenue Jean-Baptiste Cl\u00e9ment, F-93430, Villetaneuse, France - France)","DM2S - D\u00e9partement de Mod\u00e9lisation des Syst\u00e8mes et Structures (DEN/DANS/DM2S CEA Saclay 91191 Gif sur Yvette - France)"],"affiliations":[{"raw_affiliation_string":"LAGA - Laboratoire Analyse, G\u00e9om\u00e9trie et Applications (Institut Galil\u00e9e, Universit\u00e9 Paris 13, 99 avenue Jean-Baptiste Cl\u00e9ment, F-93430, Villetaneuse, France - France)","institution_ids":["https://openalex.org/I4210102686","https://openalex.org/I4210091279"]},{"raw_affiliation_string":"DM2S - D\u00e9partement de Mod\u00e9lisation des Syst\u00e8mes et Structures (DEN/DANS/DM2S CEA Saclay 91191 Gif sur Yvette - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210127723","https://openalex.org/I4210128565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071878696"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.983,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.96244484,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"45","issue":"3","first_page":"1142","last_page":"1174"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/curl","display_name":"Curl (programming language)","score":0.8935966491699219},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.8470764756202698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8121784925460815},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6677255630493164},{"id":"https://openalex.org/keywords/differential-form","display_name":"Differential form","score":0.5891767740249634},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5409172177314758},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.49283623695373535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4318801760673523},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3750763237476349},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2828527092933655},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2024056315422058},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08372363448143005}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.8935966491699219},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.8470764756202698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8121784925460815},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6677255630493164},{"id":"https://openalex.org/C115071613","wikidata":"https://www.wikidata.org/wiki/Q1047080","display_name":"Differential form","level":2,"score":0.5891767740249634},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5409172177314758},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.49283623695373535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4318801760673523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3750763237476349},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2828527092933655},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2024056315422058},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08372363448143005},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/060655031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060655031","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:CiteSeerX.psu:10.1.1.613.82","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.613.82","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.univ-lyon1.fr/~delcourte/Publications/div_rot_ddfv.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:cea-02341906v1","is_oa":false,"landing_page_url":"https://cea.hal.science/cea-02341906","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2007, 45, ⟨10.1137/060655031⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-00635633v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00635633","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2007, 45 (3), pp.1142-1174. ⟨10.1137/060655031⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-00868431v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00868431","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2007, 45 (3), pp.1142-1174","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W129017765","https://openalex.org/W1549697369","https://openalex.org/W1674659126","https://openalex.org/W1968096687","https://openalex.org/W2000450704","https://openalex.org/W2025734987","https://openalex.org/W2060076025","https://openalex.org/W2063049785","https://openalex.org/W2075224881","https://openalex.org/W2076803506","https://openalex.org/W2081729435","https://openalex.org/W2090754443","https://openalex.org/W2091221772","https://openalex.org/W2101501899","https://openalex.org/W2106141466","https://openalex.org/W2107487126","https://openalex.org/W2129867240","https://openalex.org/W2150991141","https://openalex.org/W2169269621","https://openalex.org/W2171283516","https://openalex.org/W2171737318","https://openalex.org/W2587081607","https://openalex.org/W2620827226"],"related_works":["https://openalex.org/W2382844561","https://openalex.org/W2083529992","https://openalex.org/W816511862","https://openalex.org/W1557607869","https://openalex.org/W2034255721","https://openalex.org/W2032446390","https://openalex.org/W2036663341","https://openalex.org/W1969045587","https://openalex.org/W4242162023","https://openalex.org/W2087849682"],"abstract_inverted_index":{"We":[0,48,56],"define":[1],"discrete":[2,17,20,26,29],"differential":[3],"operators":[4,18],"such":[5],"as":[6],"gradient,":[7],"divergence,":[8],"and":[9,35,42,93],"curl,":[10],"on":[11,61,81],"general":[12],"two\u2010dimensional":[13],"nonorthogonal":[14],"meshes.":[15,97],"These":[16],"verify":[19],"analogues":[21],"of":[22,32,64,78,84,87],"usual":[23],"continuous":[24],"theorems:":[25],"Green":[27],"formulae,":[28],"Hodge":[30],"decomposition":[31],"vector":[33,36],"fields,":[34],"curls":[37],"have":[38,44],"a":[39,45],"vanishing":[40,46],"divergence":[41],"gradients":[43],"curl.":[47],"apply":[49],"these":[50,65],"ideas":[51],"to":[52],"discretize":[53],"div\u2010curl":[54],"systems.":[55],"give":[57],"error":[58],"estimates":[59],"based":[60],"the":[62,71,76,79],"reformulation":[63],"systems":[66],"into":[67],"equivalent":[68],"equations":[69],"for":[70],"potentials.":[72],"Numerical":[73],"results":[74],"illustrate":[75],"use":[77],"method":[80],"several":[82],"types":[83],"meshes,":[85],"some":[86],"which":[88],"are":[89],"degenerating":[90],"triangular":[91],"meshes":[92],"nonconforming":[94],"locally":[95],"refined":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}