2009/06/09 by Georgios T. Kossioris, Kossioris, Georgios T., Georgios E. Zouraris +1
Computer Science · Economics, Econometrics and Finance · Engineering · #65C20 #65M15 #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0906.1828
openalex publication_date 2009/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C1 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.