Finite Element Approximations for a linear Cahn-Hilliard-Cook equation\n driven by the space derivative of a space-time white noise

2012/05/19 by Georgios T. Kossioris, Kossioris, Georgios T., Georgios E. Zouraris +1
Economics, Econometrics and Finance · #65C20 #65M15 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1205.4314

openalex publication_date 2012/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an initial- and Dirichlet boundary- value problem for a linear\nCahn-Hilliard-Cook equation, in one space dimension, forced by the space\nderivative of a space-time white noise. First, we propose an approximate\nregularized stochastic parabolic problem discretizing the noise using linear\nsplines. Then fully-discrete approximations to the solution of the regularized\nproblem are constructed using, for the discretization in space, a Galerkin\nfinite element method based on H2-piecewise polynomials, and, for\ntime-stepping, the Backward Euler method. Finally, we derive strong a priori\nestimates for the modeling error and for the numerical approximation error to\nthe solution of the regularized problem.\n

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