{"id":"https://openalex.org/W1935825599","doi":"https://doi.org/10.1090/mcom/3180","title":"A Hybrid High-Order method for Leray\u2013Lions elliptic equations on general meshes","display_name":"A Hybrid High-Order method for Leray\u2013Lions elliptic equations on general meshes","publication_year":2016,"publication_date":"2016-05-26","ids":{"openalex":"https://openalex.org/W1935825599","doi":"https://doi.org/10.1090/mcom/3180","mag":"1935825599"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3180","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3180","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03180-4/S0025-5718-2016-03180-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03180-4/S0025-5718-2016-03180-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037714004","display_name":"Daniele A. Di Pietro","orcid":"https://orcid.org/0000-0003-0959-8830"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniele Di Pietro","raw_affiliation_strings":["University of Montpellier, Institut Montp\u00c3\u00a9llierain Alexander Grothendieck, 34095 Montpellier, France","University of Montpellier, Institut Montp\u00e9llierain Alexander Grothendieck, 34095 Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Montpellier, Institut Montp\u00c3\u00a9llierain Alexander Grothendieck, 34095 Montpellier, France","institution_ids":["https://openalex.org/I19894307"]},{"raw_affiliation_string":"University of Montpellier, Institut Montp\u00e9llierain Alexander Grothendieck, 34095 Montpellier, France","institution_ids":["https://openalex.org/I19894307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075602113","display_name":"J\u00e9r\u00f4me Droniou","orcid":"https://orcid.org/0000-0002-3339-3053"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Droniou","raw_affiliation_strings":["School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia","SCHOOL OF MATHEMATICAL SCIENCES; MONASH UNIVERSITY; CLAYTON VICTORIA 3800 AUSTRALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"SCHOOL OF MATHEMATICAL SCIENCES; MONASH UNIVERSITY; CLAYTON VICTORIA 3800 AUSTRALIA","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.822,"has_fulltext":true,"cited_by_count":116,"citation_normalized_percentile":{"value":0.99498623,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"86","issue":"307","first_page":"2159","last_page":"2191"},"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":1.0,"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":1.0,"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":0.9991000294685364,"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":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.865373969078064},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.8351086974143982},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.7324727773666382},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6274992227554321},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5572574138641357},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5253892540931702},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5215315818786621},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4740545451641083},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.459824800491333},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.424582302570343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38045546412467957},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3758205771446228},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13364019989967346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10149917006492615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.865373969078064},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.8351086974143982},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.7324727773666382},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6274992227554321},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5572574138641357},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5253892540931702},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5215315818786621},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4740545451641083},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.459824800491333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.424582302570343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38045546412467957},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3758205771446228},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13364019989967346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10149917006492615},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3180","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3180","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03180-4/S0025-5718-2016-03180-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01183484v3","is_oa":true,"landing_page_url":"https://hal.science/hal-01183484","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":"Mathematics of Computation, 2016, 86 (307), pp.2159-2191. &#x27E8;10.1090/mcom/3180&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1090/mcom/3180","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3180","pdf_url":"https://www.ams.org/mcom/2017-86-307/S0025-5718-2016-03180-4/S0025-5718-2016-03180-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6502955777","display_name":"Hybrid High-Order Methods on polyhedral Meshes","funder_award_id":"ANR-15-CE40-0005","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1935825599.pdf","grobid_xml":"https://content.openalex.org/works/W1935825599.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W628726389","https://openalex.org/W1009522003","https://openalex.org/W1505122975","https://openalex.org/W1555674425","https://openalex.org/W1565460255","https://openalex.org/W1849648059","https://openalex.org/W1966928904","https://openalex.org/W1967077838","https://openalex.org/W1968754888","https://openalex.org/W1973533784","https://openalex.org/W1976962292","https://openalex.org/W1979771104","https://openalex.org/W1982576260","https://openalex.org/W1990258816","https://openalex.org/W1993077381","https://openalex.org/W1993348678","https://openalex.org/W1998894128","https://openalex.org/W2007699516","https://openalex.org/W2010507423","https://openalex.org/W2020718081","https://openalex.org/W2022525937","https://openalex.org/W2029725158","https://openalex.org/W2036739759","https://openalex.org/W2039955529","https://openalex.org/W2041458840","https://openalex.org/W2045686441","https://openalex.org/W2056923080","https://openalex.org/W2063884077","https://openalex.org/W2067411679","https://openalex.org/W2069951215","https://openalex.org/W2072114110","https://openalex.org/W2073237186","https://openalex.org/W2073873112","https://openalex.org/W2081513515","https://openalex.org/W2093189121","https://openalex.org/W2107487126","https://openalex.org/W2113505318","https://openalex.org/W2114612290","https://openalex.org/W2115096874","https://openalex.org/W2122838361","https://openalex.org/W2125919303","https://openalex.org/W2126086928","https://openalex.org/W2130763970","https://openalex.org/W2143430600","https://openalex.org/W2155061016","https://openalex.org/W2161530217","https://openalex.org/W2165659470","https://openalex.org/W2168914934","https://openalex.org/W2281674677","https://openalex.org/W2322620490","https://openalex.org/W2415509676","https://openalex.org/W2573899171","https://openalex.org/W3020991820","https://openalex.org/W3204708751","https://openalex.org/W4242794827","https://openalex.org/W4250831033","https://openalex.org/W4285719527","https://openalex.org/W4302995583","https://openalex.org/W4392818294"],"related_works":["https://openalex.org/W1557607869","https://openalex.org/W2487640660","https://openalex.org/W2612526717","https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2366350639","https://openalex.org/W4252969132","https://openalex.org/W2000020320","https://openalex.org/W2805799113","https://openalex.org/W1977876013"],"abstract_inverted_index":{"In":[0],"this":[1,76,104],"work,":[2],"we":[3],"develop":[4,85],"and":[5,30,50,100,110,139,192,212],"analyze":[6],"a":[7,47,51,72,86],"Hybrid":[8],"High-Order":[9],"(HHO)":[10],"method":[11,19,101,211],"for":[12,26,113,167,195,208],"steady":[13],"nonlinear":[14],"Leray\u2013Lions":[15],"problems.":[16],"The":[17,65],"proposed":[18],"has":[20,81],"several":[21],"assets,":[22],"including":[23],"the":[24,44,57,62,97,205,209],"support":[25],"arbitrary":[27],"approximation":[28],"orders":[29],"general":[31],"polytopal":[32],"meshes.":[33],"This":[34],"is":[35,68],"achieved":[36],"by":[37],"combining":[38],"two":[39],"key":[40],"ingredients":[41],"devised":[42],"at":[43],"local":[45,114],"level:":[46],"gradient":[48],"reconstruction":[49],"high-order":[52],"stabilization":[53],"term":[54],"that":[55],"generalizes":[56],"one":[58],"originally":[59],"introduced":[60],"in":[61,103],"linear":[63],"case.":[64],"convergence":[66],"analysis":[67,91],"carried":[69],"out":[70],"using":[71],"compactness":[73],"technique.":[74],"Extending":[75],"technique":[77],"to":[78,84,203],"HHO":[79],"methods":[80],"prompted":[82],"us":[83],"set":[87],"of":[88],"discrete":[89],"functional":[90],"tools":[92],"whose":[93],"interest":[94],"goes":[95],"beyond":[96],"specific":[98],"problem":[99],"addressed":[102],"work:":[105],"(direct":[106],"and)":[107],"reverse":[108],"Lebesgue":[109],"Sobolev":[111,193],"embeddings":[112,194],"polynomial":[115,197],"spaces,":[116,191],"<inline-formula":[117,140,168],"content-type=\"math/mathml\">":[118,141,169],"<mml:math":[119,142,170],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[120,143,171],"alttext=\"upper":[121,144,172],"L":[122,173],"Superscript":[123,146],"p\">":[124,149],"<mml:semantics>":[125,150,175],"<mml:msup>":[126,151,176],"<mml:mi>L</mml:mi>":[127,177],"<mml:mrow":[128,153,178],"class=\"MJX-TeXAtom-ORD\">":[129,154,179],"<mml:mi>p</mml:mi>":[130,157],"</mml:mrow>":[131,158,181],"</mml:msup>":[132,159,182],"<mml:annotation":[133,160,183],"encoding=\"application/x-tex\">L^{p}</mml:annotation>":[134],"</mml:semantics>":[135,162,185],"</mml:math>":[136,163,186],"</inline-formula>":[137,164,187],"-stability":[138],"W":[145],"s":[147],"comma":[148],"<mml:mi>W</mml:mi>":[152],"<mml:mi>s</mml:mi>":[155],"<mml:mo>,</mml:mo>":[156],"encoding=\"application/x-tex\">W^{s,p}</mml:annotation>":[161],"-approximation":[165],"properties":[166],"squared\">":[174],"<mml:mn>2</mml:mn>":[180],"encoding=\"application/x-tex\">L^{2}</mml:annotation>":[184],"-projectors":[188],"on":[189],"such":[190],"hybrid":[196],"spaces.":[198],"Numerical":[199],"tests":[200],"are":[201],"presented":[202],"validate":[204],"theoretical":[206],"results":[207],"original":[210],"variants":[213],"thereof.":[214]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}