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arXiv · 0906.1828

Fully-Discrete Finite Element Approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise: II. 2D and 3D Case

Georgios T. Kossioris·Georgios E. Zouraris
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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 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.

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Georgios T. Kossioris, Georgios E. Zouraris. 2009-06-09. Fully-Discrete Finite Element Approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise: II. 2D and 3D Case. https://arxiv.org/abs/0906.1828

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