{"corpus_id":14590647,"paper_sha":"363ae79f87e917890aa0143547ba1b3b8c5a58b4","doi":null,"arxiv_id":"0906.1828","pmid":null,"pmcid":null,"mag_id":1502885047,"dblp_id":null,"acl_id":null,"title":"Fully-Discrete Finite Element Approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise: II. 2D and 3D Case","year":2009,"publication_date":"2009-06-09","venue":"","journal":{"name":"arXiv: Numerical Analysis","pages":null,"volume":""},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics","Engineering"],"reference_count":24,"citation_count":22,"influential_citation_count":2,"is_open_access":false,"arxiv_categories":["math.NA"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"We consider an initial- and Dirichlet boundary- value problem for a fourth-order linear stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a modeling error is introduced and a regularized fourth- order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a standard Galerkin finite element method based on C 1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modeling error and for the approximation error to the solution of the regularized problem.","claims":[{"public_id":"cl_755ca8d2d1fc4630b4ffdb86f99ecca7","status":"active","text":"Discretizing the space-time white noise introduces a modeling error and yields a regularized fourth-order linear stochastic parabolic problem.","confidence":0.95,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_755ca8d2d1fc4630b4ffdb86f99ecca7"},{"public_id":"cl_da68704a18b7551d852236dd4b4b9791","status":"active","text":"Fully-discrete approximations are constructed using a standard Galerkin finite element method with C1 piecewise polynomials for space discretization and the Backward Euler method 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