{"id":"https://openalex.org/W7148540425","doi":"https://doi.org/10.48550/arxiv.2604.00861","title":"Error Estimates for Nitsche's Method on Approximate Domains","display_name":"Error Estimates for Nitsche's Method on Approximate Domains","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148540425","doi":"https://doi.org/10.48550/arxiv.2604.00861"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.00861","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00861","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":null,"license_id":null,"version":null,"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":"https://doi.org/10.48550/arxiv.2604.00861","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077614976","display_name":"Mats G. Larson","orcid":"https://orcid.org/0000-0001-5589-4521"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larson, Mats G.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132820079","display_name":"Karl Larsson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Larsson, Karl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084747821","display_name":"Shantiram Mahata","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mahata, Shantiram","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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":0.7430999875068665,"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":0.7430999875068665,"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":0.16359999775886536,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.022299999371170998,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.6890000104904175},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6506999731063843},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5353999733924866},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5145000219345093},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5052000284194946},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.48500001430511475},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4652999937534332}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7019000053405762},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6890000104904175},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6506999731063843},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5353999733924866},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5145000219345093},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.436599999666214},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4278999865055084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42750000953674316},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29840001463890076},{"id":"https://openalex.org/C118732077","wikidata":"https://www.wikidata.org/wiki/Q273176","display_name":"Normal","level":3,"score":0.29280000925064087},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.00861","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00861","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.00861","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00861","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,44,87],"derive":[1],"a":[2,90,99,121,131,144,180],"priori":[3],"error":[4],"estimates":[5],"for":[6,19,197],"Nitsche's":[7],"method":[8],"applied":[9],"to":[10,160,175],"elliptic":[11],"problems":[12],"on":[13,120],"approximate":[14],"domains.":[15],"Such":[16],"approximations":[17],"arise,":[18],"example,":[20],"in":[21,48,61,189],"unfitted":[22,198],"finite":[23,191],"element":[24,192],"methods,":[25,193],"data-driven":[26],"simulations,":[27],"and":[28,53,56,108,167,170],"evolving":[29],"domain":[30,35],"problems,":[31],"where":[32,125],"the":[33,41,59,71,83,126,137,148,150,163,171],"computational":[34],"does":[36],"not":[37],"coincide":[38],"exactly":[39],"with":[40,102,194],"physical":[42],"one.":[43],"quantify":[45],"geometric":[46,185],"errors":[47,156],"terms":[49],"of":[50,82,183],"boundary":[51,84,106,154],"location":[52,85,107,155,166],"normal":[54,109,161,168,176],"perturbations":[55],"carry":[57],"out":[58],"analysis":[60],"an":[62,76,79,114],"abstract":[63],"CutFEM":[64],"framework":[65],"under":[66],"standard":[67],"stability":[68],"assumptions.":[69],"In":[70],"energy":[72,151],"norm,":[73],"we":[74,112],"obtain":[75],"estimate":[77,93,118],"exhibiting":[78],"$h^{-1/2}$":[80],"amplification":[81],"error.":[86],"then":[88],"prove":[89],"refined":[91,122],"$H^1$-seminorm":[92,164],"that":[94],"removes":[95],"this":[96],"amplification,":[97],"yielding":[98],"sharper":[100],"bound":[101],"additive":[103,133],"contributions":[104],"from":[105,136],"errors.":[110],"Finally,":[111],"establish":[113],"optimal":[115],"order":[116],"$L^2$-error":[117],"based":[119],"duality":[123],"argument,":[124],"geometry":[127],"contribution":[128],"appears":[129],"as":[130],"separate":[132],"term,":[134],"decoupled":[135],"mesh":[138],"size":[139],"$h$.":[140],"The":[141],"results":[142],"reveal":[143],"fundamental":[145],"distinction":[146],"between":[147],"norms:":[149],"norm":[152],"amplifies":[153],"while":[157],"remaining":[158],"insensitive":[159,174],"perturbations,":[162],"separates":[165],"errors,":[169],"$L^2$-norm":[172],"is":[173],"perturbations.":[177],"This":[178],"provides":[179],"clear":[181],"characterization":[182],"how":[184],"approximation":[186],"affects":[187],"convergence":[188],"Nitsche-based":[190],"particular":[195],"relevance":[196],"discretizations.":[199]},"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2026-04-03T00:00:00"}