{"id":"https://openalex.org/W2498187621","doi":"https://doi.org/10.1137/15m1053098","title":"Crank--Nicolson Finite Element Approximations for a Linear Stochastic Fourth Order Equation with Additive Space-Time White Noise","display_name":"Crank--Nicolson Finite Element Approximations for a Linear Stochastic Fourth Order Equation with Additive Space-Time White Noise","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2498187621","doi":"https://doi.org/10.1137/15m1053098","mag":"2498187621"},"language":"en","primary_location":{"id":"doi:10.1137/15m1053098","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1053098","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.05206","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075381508","display_name":"Georgios E. Zouraris","orcid":"https://orcid.org/0000-0003-0234-0175"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Georgios E. Zouraris","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075381508"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00874647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"56","issue":"2","first_page":"838","last_page":"858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9972000122070312,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8069405555725098},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6883591413497925},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6185140609741211},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5445156693458557},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.5214059352874756},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.509067952632904},{"id":"https://openalex.org/keywords/spectral-element-method","display_name":"Spectral element method","score":0.4766450822353363},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.46925660967826843},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46396246552467346},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.4560643434524536},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4361172914505005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8069405555725098},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6883591413497925},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6185140609741211},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5445156693458557},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.5214059352874756},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.509067952632904},{"id":"https://openalex.org/C38961997","wikidata":"https://www.wikidata.org/wiki/Q7575186","display_name":"Spectral element method","level":4,"score":0.4766450822353363},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.46925660967826843},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46396246552467346},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4560643434524536},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4361172914505005},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/15m1053098","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1053098","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.05206","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.05206","pdf_url":"https://arxiv.org/pdf/1607.05206","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2498187621","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1709.08496.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1607.05206","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1607.05206","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":"pmh:oai:arXiv.org:1607.05206","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.05206","pdf_url":"https://arxiv.org/pdf/1607.05206","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1335521237","display_name":null,"funder_award_id":"Research Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3998201246","display_name":null,"funder_award_id":"Social","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G5374134968","display_name":null,"funder_award_id":"European Social Fund","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8557630580","display_name":null,"funder_award_id":"co-financed","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2498187621.pdf","grobid_xml":"https://content.openalex.org/works/W2498187621.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1502885047","https://openalex.org/W1527296550","https://openalex.org/W1532277156","https://openalex.org/W1597209545","https://openalex.org/W1967323436","https://openalex.org/W1968339027","https://openalex.org/W1978697444","https://openalex.org/W1998633397","https://openalex.org/W2020169924","https://openalex.org/W2024999953","https://openalex.org/W2041422028","https://openalex.org/W2055093138","https://openalex.org/W2059086491","https://openalex.org/W2062796292","https://openalex.org/W2082621526","https://openalex.org/W2086193016","https://openalex.org/W2123625882","https://openalex.org/W2142800562","https://openalex.org/W2163511969","https://openalex.org/W2328632875","https://openalex.org/W2963221471","https://openalex.org/W4247755366"],"related_works":["https://openalex.org/W2044549253","https://openalex.org/W2121676774","https://openalex.org/W2753255166","https://openalex.org/W2485333778","https://openalex.org/W1225207327","https://openalex.org/W2896973197","https://openalex.org/W2725660858","https://openalex.org/W1969748759","https://openalex.org/W1982409348","https://openalex.org/W1537622266","https://openalex.org/W2767697744","https://openalex.org/W1965791898","https://openalex.org/W2479718646","https://openalex.org/W2084633442","https://openalex.org/W2017810710","https://openalex.org/W3157980825","https://openalex.org/W3196680107","https://openalex.org/W2766295403","https://openalex.org/W2322075191","https://openalex.org/W11545334"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,11,72,128],"model":[3],"initial":[4],"and":[5,126],"Dirichlet":[6],"boundary":[7],"value":[8],"problem":[9,44,62],"for":[10,67,83,134],"fourth":[12,40],"order":[13,41],"linear":[14],"stochastic":[15,42,50],"parabolic":[16,43],"equation":[17],"in":[18,70],"one":[19],"space":[20],"dimension,":[21],"forced":[22],"by":[23,34,65],"an":[24,38],"additive":[25],"space-time":[26],"white":[27],"noise.":[28],"First,":[29],"we":[30,93],"approximate":[31,61],"its":[32],"solution":[33,36,58],"the":[35,57,60,68,85,89,109,115,119,137],"of":[37,56,102],"auxiliary":[39],"with":[45],"additive,":[46],"finite":[47,75],"dimensional,":[48],"spectral-type":[49],"load.":[51],"Then,":[52],"fully":[53],"discrete":[54],"approximations":[55],"to":[59,114],"are":[63],"constructed":[64],"using,":[66],"discretization":[69,91,110],"space,":[71],"standard":[73],"Galerkin":[74],"element":[76],"method":[77,121],"based":[78],"on":[79,108],"$H^2$-piecewise":[80],"polynomials":[81],"and,":[82],"time-stepping,":[84],"Crank--Nicolson":[86,120],"method.":[87],"Analyzing":[88],"proposed":[90],"approach,":[92],"derive":[94],"strong":[95],"error":[96],"estimates":[97],"that":[98],"establish":[99],"optimal":[100],"rate":[101],"convergence":[103,138],"without":[104],"imposing":[105],"CFL":[106],"conditions":[107],"parameters.":[111],"In":[112],"contrast":[113],"backward":[116],"Euler":[117],"method,":[118],"is":[122,132],"not":[123],"strongly":[124],"$A(\\vartheta)$-stable,":[125],"thus":[127],"different":[129],"stability":[130],"argument":[131],"required":[133],"building":[135],"up":[136],"analysis.":[139]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}