{"id":"https://openalex.org/W4417035279","doi":"https://doi.org/10.48550/arxiv.2512.04003","title":"Mixed finite element approximation for non-divergence form elliptic equations with random input data","display_name":"Mixed finite element approximation for non-divergence form elliptic equations with random input data","publication_year":2025,"publication_date":"2025-12-03","ids":{"openalex":"https://openalex.org/W4417035279","doi":"https://doi.org/10.48550/arxiv.2512.04003"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.04003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.04003","pdf_url":"https://arxiv.org/pdf/2512.04003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.04003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030966073","display_name":"Amireh Mousavi","orcid":"https://orcid.org/0000-0001-8748-6901"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mousavi, Amireh","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030966073"],"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.8910999894142151,"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":0.8910999894142151,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.01810000091791153,"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":0.016899999231100082,"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/discretization","display_name":"Discretization","score":0.6870999932289124},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5967000126838684},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.536300003528595},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4708999991416931},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.4537000060081482},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.42649999260902405},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.3978999853134155},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.38040000200271606},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.3799999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7656999826431274},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6870999932289124},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5967000126838684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5400000214576721},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.536300003528595},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4537000060081482},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4142000079154968},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.3799999952316284},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.37599998712539673},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.31380000710487366},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2734000086784363},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.26089999079704285},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.04003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.04003","pdf_url":"https://arxiv.org/pdf/2512.04003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},{"id":"doi:10.48550/arxiv.2512.04003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.04003","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:oai:arXiv.org:2512.04003","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.04003","pdf_url":"https://arxiv.org/pdf/2512.04003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417035279.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,102],"consider":[1],"an":[2,95,136],"elliptic":[3],"partial":[4],"differential":[5],"equation":[6,111],"in":[7,30,39,80],"non-divergence":[8],"form":[9],"with":[10,35,150],"a":[11,24,36,50,72,90,125,137],"random":[12,16],"diffusion":[13],"matrix":[14],"and":[15,93,163],"forcing":[17],"term.":[18],"To":[19],"address":[20],"this,":[21],"we":[22,47,88,134],"propose":[23],"mixed-type":[25],"continuous":[26,56],"finite":[27],"element":[28],"discretization":[29,38,154],"the":[31,40,44,55,65,81,104,109,113,142,147,153,165],"physical":[32],"domain,":[33],"combined":[34],"collocation":[37,105],"stochastic":[41,51,110],"domain.":[42],"For":[43],"mixed":[45],"formulation,":[46],"first":[48],"introduce":[49],"cost":[52,74],"functional":[53],"at":[54,112],"level.":[57],"This":[58,121],"formulation":[59],"is":[60],"then":[61],"enhanced":[62],"to":[63,124,152,161],"incorporate":[64],"vanishing":[66],"tangential":[67],"trace":[68],"constraint":[69],"directly":[70],"into":[71],"mesh-dependent":[73,91],"functional,":[75],"rather":[76],"than":[77],"enforcing":[78],"it":[79],"solution's":[82],"function":[83],"space.":[84],"In":[85],"this":[86,100],"context,":[87],"define":[89],"norm":[92],"provide":[94],"error":[96,139],"analysis":[97],"based":[98],"on":[99],"norm.":[101],"employ":[103],"method":[106],"by":[107],"collocating":[108],"zeros":[114],"of":[115,127],"suitable":[116],"tensor":[117],"product":[118],"orthogonal":[119],"polynomials.":[120],"approach":[122],"leads":[123],"system":[126],"uncoupled":[128],"deterministic":[129],"problems,":[130],"simplifying":[131],"computation.":[132],"Furthermore,":[133],"establish":[135],"poriori":[138],"bound":[140],"for":[141],"fully":[143],"discrete":[144],"approximation,":[145],"detailing":[146],"convergence":[148],"rates":[149],"respect":[151],"parameters.":[155],"Finally,":[156],"numerical":[157],"results":[158],"are":[159],"presented":[160],"confirm":[162],"validate":[164],"theoretical":[166],"findings.":[167]},"counts_by_year":[],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-12-05T00:00:00"}
