{"id":"https://openalex.org/W7222394620","doi":"https://doi.org/10.48550/arxiv.2610.21611","title":"A priori error estimates for a Hybrid High-Order method on variable-exponent Leray-Lions problems","display_name":"A priori error estimates for a Hybrid High-Order method on variable-exponent Leray-Lions problems","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222394620","doi":"https://doi.org/10.48550/arxiv.2610.21611"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.21611","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21611","pdf_url":"https://arxiv.org/pdf/2610.21611","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.21611","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065456667","display_name":"Andr\u00e9 Harnist","orcid":"https://orcid.org/0000-0002-7896-5764","observed_orcids":["https://orcid.org/0000-0002-7896-5764"]},"institutions":[{"id":"https://openalex.org/I102516824","display_name":"Universit\u00e9 de Technologie de Compi\u00e8gne","ror":"https://ror.org/04y5kwa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I102516824"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4405260806","display_name":"Laboratoire de math\u00e9matiques appliqu\u00e9es de Compi\u00e8gne","ror":"https://ror.org/049z3x013","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102516824","https://openalex.org/I4405260806"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Harnist, Andr\u00e9","raw_affiliation_strings":["Universit\u00e9 de technologie de Compi\u00e8gne , Alliance Sorbonne Universit\u00e9 , LMAC , Compi\u00e8gne , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de technologie de Compi\u00e8gne , Alliance Sorbonne Universit\u00e9 , LMAC , Compi\u00e8gne , France","institution_ids":["https://openalex.org/I102516824","https://openalex.org/I39804081","https://openalex.org/I4405260806"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5116186611","display_name":"Romain Mottier","orcid":"https://orcid.org/0009-0001-2967-7694","observed_orcids":["https://orcid.org/0009-0001-2967-7694"]},"institutions":[{"id":"https://openalex.org/I1850255","display_name":"University of Basel","ror":"https://ror.org/02s6k3f65","country_code":"CH","type":"education","lineage":["https://openalex.org/I1850255"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mottier, Romain","raw_affiliation_strings":["University of Basel , Department of Mathematics and Computer Science , Basel , Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Basel , Department of Mathematics and Computer Science , Basel , Switzerland","institution_ids":["https://openalex.org/I1850255"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9990000128746033,"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":0.9990000128746033,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":9.999999747378752e-05,"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/hybrid-high-order-method","display_name":"hybrid high-order method","score":0.8790000081062317},{"id":"https://openalex.org/keywords/a-priori-error-estimates","display_name":"a priori error estimates","score":0.9829999804496765},{"id":"https://openalex.org/keywords/leray-lions-operators","display_name":"Leray-Lions operators","score":0.9279999732971191},{"id":"https://openalex.org/keywords/nonconforming-finite-elements","display_name":"nonconforming finite elements","score":0.6079999804496765},{"id":"https://openalex.org/keywords/voronoi-meshes","display_name":"Voronoi meshes","score":0.6959999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.751800000667572},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6985999941825867},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6930999755859375},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6478999853134155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6478000283241272},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6119999885559082},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42320001125335693},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.3984000086784363},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.39590001106262207},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.3928999900817871},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3147999942302704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.2784000039100647},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.21611","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21611","pdf_url":"https://arxiv.org/pdf/2610.21611","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-05801004v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05801004","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.21611","doi":"https://doi.org/10.48550/arxiv.2610.21611","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.21611","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.21611","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21611","pdf_url":"https://arxiv.org/pdf/2610.21611","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222394620.pdf","grobid_xml":"https://content.openalex.org/works/W7222394620.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W931854690","https://openalex.org/W1482163423","https://openalex.org/W1935825599","https://openalex.org/W1981146595","https://openalex.org/W1982576260","https://openalex.org/W1998894128","https://openalex.org/W2017874222","https://openalex.org/W2038490905","https://openalex.org/W2044303806","https://openalex.org/W2072741826","https://openalex.org/W2091486840","https://openalex.org/W2102844628","https://openalex.org/W2116404756","https://openalex.org/W2122838361","https://openalex.org/W2153317684","https://openalex.org/W2165659470","https://openalex.org/W2168914934","https://openalex.org/W2244987555","https://openalex.org/W2285094888","https://openalex.org/W2301589764","https://openalex.org/W2465859507","https://openalex.org/W2883313970","https://openalex.org/W2950034650","https://openalex.org/W2963532308","https://openalex.org/W3013208380","https://openalex.org/W3109170755","https://openalex.org/W3112274847","https://openalex.org/W3172168456","https://openalex.org/W3175761886","https://openalex.org/W4224216082","https://openalex.org/W4231001225","https://openalex.org/W4386991616","https://openalex.org/W4399172437","https://openalex.org/W4399374999","https://openalex.org/W4399378878","https://openalex.org/W7129724855","https://openalex.org/W7163903653"],"related_works":["https://openalex.org/W3112274847","https://openalex.org/W7222456712","https://openalex.org/W4403116272","https://openalex.org/W1935825599","https://openalex.org/W2409376292","https://openalex.org/W4385284980","https://openalex.org/W3133821104","https://openalex.org/W2612085284","https://openalex.org/W2510573815","https://openalex.org/W2999161263"],"abstract_inverted_index":{"We":[0],"derive":[1,87],"a":[2,18,55,66,88],"priori":[3],"error":[4,57],"estimates":[5],"for":[6,128],"the":[7,26,47,61,72,82,93,98,104,114,155,161,165],"Hybrid":[8],"High-Order":[9],"(HHO)":[10],"discretization":[11],"of":[12,28,39,46,123],"variable-exponent":[13,120],"Leray--Lions":[14],"problems":[15],"introduced":[16],"in":[17],"companion":[19],"convergence":[20],"study.":[21],"HHO":[22],"methods":[23],"belong":[24],"to":[25],"family":[27],"hybrid":[29],"nonconforming":[30],"methods,":[31],"based":[32],"on":[33,119,149,164],"cell":[34],"and":[35,50,65,77,102,132,141,151,158],"face":[36],"polynomial":[37,106,124,130],"unknowns":[38],"arbitrary":[40],"degree.":[41],"Under":[42],"additional":[43],"broken":[44],"regularity":[45,162],"exact":[48],"solution":[49],"its":[51],"flux,":[52],"we":[53,85],"establish":[54],"localized":[56],"estimate":[58,68],"that":[59,91,109,160],"retains":[60],"individual":[62],"element":[63],"sizes":[64],"global":[67],"whose":[69],"rate":[70],"distinguishes":[71],"purely":[73,78],"subquadratic,":[74],"mixed":[75],"subquadratic--superquadratic,":[76],"superquadratic":[79],"regimes.":[80],"In":[81],"subquadratic":[83],"range,":[84],"also":[86,138],"regime-dependent":[89],"refinement":[90],"compares":[92],"local":[94,99],"approximation":[95,121],"scale":[96,101,110],"with":[97],"non-degeneracy":[100],"recovers":[103],"optimal":[105],"order":[107],"when":[108],"is":[111],"resolved":[112],"by":[113],"mesh.":[115],"The":[116,136],"analysis":[117],"relies":[118],"properties":[122],"projectors,":[125],"mean-exponent":[126],"tools":[127],"discrete":[129],"spaces,":[131],"weighted":[133],"monotonicity":[134],"estimates.":[135],"framework":[137],"covers":[139],"regularized":[140],"mildly":[142],"non-symmetric":[143],"anisotropic":[144],"Carreau--Yasuda-type":[145],"fluxes.":[146],"Numerical":[147],"experiments":[148],"Cartesian":[150],"Voronoi":[152],"meshes":[153],"support":[154],"predicted":[156],"rates":[157],"show":[159],"assumption":[163],"flux":[166],"cannot":[167],"be":[168],"dispensed":[169],"with.":[170]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-17T00:00:00"}
