{"id":"https://openalex.org/W7134971464","doi":"https://doi.org/10.48550/arxiv.2603.09449","title":"Exponential Convergence of $hp$-FEM for the Integral Fractional Laplacian on cuboids","display_name":"Exponential Convergence of $hp$-FEM for the Integral Fractional Laplacian on cuboids","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134971464","doi":"https://doi.org/10.48550/arxiv.2603.09449"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.09449","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09449","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.2603.09449","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038044982","display_name":"Bj\u00f6rn Bahr","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bahr, Bj\u00f6rn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019645947","display_name":"Markus Faustmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Faustmann, Markus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083328576","display_name":"Carlo Marcati","orcid":"https://orcid.org/0000-0002-0313-5387"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcati, Carlo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Melenk, Jens Markus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128728847","display_name":"Christoph Schwab","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schwab, Christoph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.2750999927520752,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.2750999927520752,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2371000051498413,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.22419999539852142,"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/sobolev-space","display_name":"Sobolev space","score":0.5616999864578247},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5037000179290771},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4758000075817108},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4672999978065491},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4429999887943268},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.44179999828338623},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41760000586509705},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.38040000200271606},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"Fractional Laplacian","score":0.3781000077724457}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184999823570251},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5616999864578247},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5238000154495239},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5037000179290771},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.44179999828338623},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3950999975204468},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C7402137","wikidata":"https://www.wikidata.org/wiki/Q778099","display_name":"Dirichlet integral","level":5,"score":0.2711000144481659},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2597000002861023}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.09449","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09449","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.2603.09449","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09449","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"the":[1,45,73],"Dirichlet":[2],"integral":[3],"fractional":[4],"Laplacian,":[5],"we":[6,34],"prove":[7,35],"root":[8],"exponential":[9],"convergence":[10],"of":[11,43,63],"tensor-product":[12],"$hp$-finite":[13],"element":[14],"approximations":[15,39],"on":[16],"$(0,1)^3$,":[17],"for":[18,36],"forcing":[19],"$f$":[20],"that":[21],"is":[22],"analytic":[23,27],"in":[24,30],"$[0,1]^3$.":[25],"Exploiting":[26],"regularity":[28],"estimates":[29],"weighted":[31],"Sobolev":[32],"spaces,":[33],"$hp$-GLL":[37],"interpolation":[38],"with":[40,69],"$N$":[41],"degrees":[42],"freedom":[44],"energy":[46],"norm":[47],"error":[48],"bound":[49],"$\\lesssim":[50],"\\exp(-b\\sqrt[6]{N})$.":[51],"Tensor":[52],"product":[53],"mesh":[54],"families":[55],"which":[56],"are":[57,65],"geometrically":[58],"refined":[59],"towards":[60],"all":[61],"sides":[62],"$(0,1)^3$":[64],"used.":[66],"Numerical":[67],"experiments":[68],"$hp$-Galerkin":[70],"FEM":[71],"confirm":[72],"bound.":[74]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-12T00:00:00"}
