{"id":"https://openalex.org/W7127886893","doi":"https://doi.org/10.48550/arxiv.2602.05698","title":"A penalized \u03d5-FEM scheme for the Poisson Dirichlet problem","display_name":"A penalized \u03d5-FEM scheme for the Poisson Dirichlet problem","publication_year":2026,"publication_date":"2026-02-05","ids":{"openalex":"https://openalex.org/W7127886893","doi":"https://doi.org/10.48550/arxiv.2602.05698"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.05698","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042999786","display_name":"Rapha\u00ebl Bulle","orcid":"https://orcid.org/0000-0002-6239-125X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bulle, Rapha\u00ebl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125116661","display_name":"Michel Duprez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Duprez, Michel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058132613","display_name":"Vanessa Lleras","orcid":"https://orcid.org/0000-0003-1358-9558"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lleras, Vanessa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066934221","display_name":"Killian Vuillemot","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vuillemot, Killian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9718999862670898,"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":0.9718999862670898,"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":0.00930000003427267,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.003800000064074993,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6297000050544739},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5485000014305115},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5343000292778015},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5008999705314636},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.49470001459121704},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4821000099182129},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44859999418258667},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.444599986076355}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936000227928162},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6237000226974487},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.49470001459121704},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4821000099182129},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.43529999256134033},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3677999973297119},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.366100013256073},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.3619000017642975},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.26989999413490295},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.2619999945163727}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.05698","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.05698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.05698","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.05698","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6930952668190002,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"analyze":[4],"a":[5,23,32,58,89,95],"penalized":[6],"variant":[7],"of":[8,35],"the":[9,13,36,40,46,50,64,67,74,78,81,103,110,123,129,134,138],"\u03d5-FEM":[10,21,48,136],"scheme":[11,85],"for":[12,42],"Poisson":[14],"equation":[15],"with":[16,132],"Dirichlet":[17],"boundary":[18,55,79],"conditions.":[19],"The":[20,84],"is":[22,70,86],"recently":[24],"introduced":[25],"unfitted":[26],"finite":[27,141],"element":[28,142],"method":[29,51,131],"based":[30],"on":[31,73],"level-set":[33,68],"description":[34],"geometry,":[37],"which":[38],"avoids":[39],"need":[41],"boundary-fitted":[43],"meshes.":[44],"Unlike":[45],"original":[47,135],"formulation,":[49],"proposed":[52,130],"here":[53],"enforces":[54],"conditions":[56],"through":[57],"penalization":[59],"term.":[60],"This":[61],"approach":[62],"has":[63],"advantage":[65],"that":[66],"function":[69],"required":[71],"only":[72],"cells":[75],"adjacent":[76],"to":[77,121,127],"in":[80,102,109],"variational":[82],"formulation.":[83],"stabilized":[87],"using":[88],"ghost":[90],"penalty":[91],"technique.":[92],"We":[93],"derive":[94],"priori":[96],"error":[97],"estimates,":[98],"showing":[99],"optimal":[100],"convergence":[101,108],"H1":[104],"semi-norm":[105],"and":[106,126,137],"quasi-optimal":[107],"L2":[111],"norm":[112],"under":[113],"suitable":[114],"regularity":[115],"assumptions.":[116],"Numerical":[117],"experiments":[118],"are":[119],"presented":[120],"validate":[122],"theoretical":[124],"results":[125],"compare":[128],"both":[133],"standard":[139],"fitted":[140],"method.":[143]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-07T00:00:00"}