{"id":"https://openalex.org/W7165181881","doi":"https://doi.org/10.48550/arxiv.2606.18678","title":"Quasi-Monte Carlo finite element approximation for singularly perturbed convection-diffusion problems with random velocity","display_name":"Quasi-Monte Carlo finite element approximation for singularly perturbed convection-diffusion problems with random velocity","publication_year":2026,"publication_date":"2026-06-17","ids":{"openalex":"https://openalex.org/W7165181881","doi":"https://doi.org/10.48550/arxiv.2606.18678"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.18678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18678","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.18678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000154710","display_name":"Seungchan Ko","orcid":"https://orcid.org/0000-0002-6199-442X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ko, Seungchan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066860206","display_name":"Guanglian Li","orcid":"https://orcid.org/0000-0003-0615-2681"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Guanglian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138868356","display_name":"Yi Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7401000261306763,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7401000261306763,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.1559000015258789,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.038600001484155655,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.650600016117096},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.5958999991416931},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5325999855995178},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.49779999256134033},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4661000072956085},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.46470001339912415},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.45820000767707825},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.423799991607666},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4171000123023987}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7552000284194946},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.650600016117096},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.5958999991416931},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5557000041007996},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5325999855995178},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47870001196861267},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.46470001339912415},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45820000767707825},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4171000123023987},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.3431999981403351},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.30570000410079956},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3041999936103821},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.2705000042915344},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.250900000333786},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.18678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18678","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.18678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.18678","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":"Preprint"},"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":{"This":[0],"paper":[1],"studies":[2],"the":[3,21,45,49,53,63,71,86,96,102,109,124,128,137],"numerical":[4,41],"approximation":[5],"of":[6,48,52,62,95,123,136],"a":[7,13,27,31,39,58,65,76,91,113,120],"singularly":[8],"perturbed":[9],"convection-diffusion":[10],"problem":[11],"over":[12,85],"bounded":[14],"polygonal":[15],"domain":[16],"in":[17,34],"$\\mathbb{R}^d$":[18],"($d=2,3$),":[19],"where":[20],"velocity":[22,73],"field":[23],"is":[24,131],"modeled":[25],"by":[26],"log-uniform":[28],"random":[29],"field,":[30,74],"setting":[32],"typical":[33],"uncertainty":[35],"quantification.":[36],"We":[37,89],"introduce":[38],"novel":[40],"framework":[42],"for":[43],"computing":[44],"expected":[46],"value":[47],"linear":[50,115],"functionals":[51],"solution.":[54],"The":[55],"approach":[56],"combines":[57],"finite":[59],"element":[60],"discretization":[61],"problem,":[64],"truncated":[66],"Karhunen--Lo\u00e8ve":[67],"expansion":[68],"to":[69,82,133],"represent":[70],"stochastic":[72],"and":[75,106],"lattice-based":[77],"quasi-Monte":[78],"Carlo":[79],"(QMC)":[80],"method":[81,111],"estimate":[83],"expectations":[84],"parameter":[87],"space.":[88],"provide":[90],"rigorous":[92],"error":[93,105],"analysis":[94],"proposed":[97],"scheme,":[98],"establishing":[99],"bounds":[100],"on":[101],"mean":[103],"squared":[104],"demonstrating":[107],"that":[108],"QMC":[110],"achieves":[112],"nearly":[114],"optimal":[116],"convergence":[117,129],"rate,":[118],"with":[119],"constant":[121],"independent":[122,135],"integration":[125],"dimension.":[126],"Furthermore,":[127],"rate":[130],"shown":[132],"be":[134],"singular":[138],"perturbation":[139],"parameter.":[140]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-19T00:00:00"}
