{"id":"https://openalex.org/W7212288167","doi":"https://doi.org/10.48550/arxiv.2609.11584","title":"Convergence of finite element approximations for the one-dimensional stochastic Burgers equation with additive trace-class noise","display_name":"Convergence of finite element approximations for the one-dimensional stochastic Burgers equation with additive trace-class noise","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212288167","doi":"https://doi.org/10.48550/arxiv.2609.11584"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11584","pdf_url":"https://arxiv.org/pdf/2609.11584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.11584","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052390530","display_name":"Binjie Li","orcid":"https://orcid.org/0000-0002-0184-6599","observed_orcids":["https://orcid.org/0000-0002-0184-6599"]},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Binjie","raw_affiliation_strings":["School of Mathematics , Sichuan University , Chengdu 610064 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Sichuan University , Chengdu 610064 , China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151338248","display_name":"Xiaoping Xie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xie, Xiaoping","raw_affiliation_strings":["School of Mathematics , Sichuan University , Chengdu 610064 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Sichuan University , Chengdu 610064 , China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151294493","display_name":"Qin Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I16351329","display_name":"China West Normal University","ror":"https://ror.org/04s99y476","country_code":"CN","type":"education","lineage":["https://openalex.org/I16351329"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhou, Qin","raw_affiliation_strings":["School of Mathematics , China West Normal University , Nanchong 637002 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , China West Normal University , Nanchong 637002 , China","institution_ids":["https://openalex.org/I16351329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.8827999830245972,"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":0.8827999830245972,"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.045499999076128006,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.009100000374019146,"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/stochastic-burgers-equation","display_name":"stochastic Burgers equation","score":0.9890000224113464},{"id":"https://openalex.org/keywords/finite-element-approximation","display_name":"finite element approximation","score":0.7919999957084656},{"id":"https://openalex.org/keywords/euler-maruyama-method","display_name":"Euler-Maruyama scheme","score":0.8100000023841858},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.5770000219345093},{"id":"https://openalex.org/keywords/fully-discrete-scheme","display_name":"fully discrete scheme","score":0.6050000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7702000141143799},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6455000042915344},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.644599974155426},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5777000188827515},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5426999926567078},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.5002999901771545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48750001192092896},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.48030000925064087},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.46320000290870667},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4413999915122986},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.4090999960899353},{"id":"https://openalex.org/C4349628","wikidata":"https://www.wikidata.org/wiki/Q17027720","display_name":"hp-FEM","level":5,"score":0.383899986743927},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.3601999878883362},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.2973000109195709},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.26600000262260437},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11584","pdf_url":"https://arxiv.org/pdf/2609.11584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.11584","doi":"https://doi.org/10.48550/arxiv.2609.11584","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11584","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11584","pdf_url":"https://arxiv.org/pdf/2609.11584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1795423594","display_name":null,"funder_award_id":"12301525","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3413728038","display_name":null,"funder_award_id":"12571434","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329861","display_name":"Natural Science Foundation of Sichuan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212288167.pdf","grobid_xml":"https://content.openalex.org/works/W7212288167.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2562967919","https://openalex.org/W2982934763","https://openalex.org/W4307937324"],"related_works":["https://openalex.org/W4391962739","https://openalex.org/W4405783969","https://openalex.org/W4307937324","https://openalex.org/W7097171277","https://openalex.org/W7096051433","https://openalex.org/W2438281611","https://openalex.org/W4396216317","https://openalex.org/W7139959487","https://openalex.org/W7171831849","https://openalex.org/W2140972750"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"finite":[3,20,87],"element":[4,21,88],"approximations":[5],"of":[6,61,106,113],"the":[7,18,74,79,85,116,126],"one-dimensional":[8],"viscous":[9],"stochastic":[10],"Burgers":[11],"equation":[12],"with":[13,32,68,92],"additive":[14],"trace-class":[15],"noise.":[16],"For":[17,78],"$P_2$":[19],"spatial":[22],"semi-discretization,":[23],"we":[24,54,99],"derive":[25,55],"strong":[26,76,102],"error":[27,57],"estimates":[28,58],"that":[29],"are":[30,122],"optimal":[31],"respect":[33],"to":[34,124],"regularity":[35],"in":[36,51,90,97,109],"\\(L^p([0,T]":[37],"\\times":[38],"\u03a9;H_{D}^{\u03b1,q})\\)":[39],"for":[40,59],"\\(p,q\\in[2,\\infty)\\)":[41],"and":[42,65],"\\(\u03b1\\in[-1,0]\\),":[43],"as":[44,46],"well":[45],"an":[47],"almost":[48],"regularity-optimal":[49],"estimate":[50],"\\(L^p(\u03a9;C([0,T];L^\\infty(\\mathcal{O})))\\).":[52],"Furthermore,":[53],"weak":[56,69],"moments":[60],"both":[62],"terminal":[63],"$L^q$-norms":[64],"space-time":[66],"$L^p(0,T;L^q(\\mathcal{O}))$-norms,":[67],"convergence":[70,104,128],"rates":[71],"(nearly)":[72],"twice":[73],"corresponding":[75],"ones.":[77],"fully":[80],"discrete":[81,111],"scheme,":[82],"which":[83],"combines":[84],"\\(P_2\\)":[86],"method":[89],"space":[91],"a":[93,101,110],"drift-implicit":[94],"Euler--Maruyama":[95],"scheme":[96],"time,":[98],"establish":[100],"temporal":[103],"rate":[105],"order":[107],"\\(\u03c4^{1/2-\\varepsilon}\\)":[108],"analogue":[112],"\\(L^p(\u03a9;C([0,T];L^\\infty(\\mathcal{O})))\\),":[114],"under":[115],"condition":[117],"\\(\u03c4\\leqslant":[118],"h^2\\).":[119],"Numerical":[120],"experiments":[121],"presented":[123],"illustrate":[125],"theoretical":[127],"rates.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}