Fully-discrete Finite Element Approximations for a Fourth-order Linear Stochastic Parabolic Equation with Additive Space-time White Noise Ii. 2d and 3d Case
نویسندگان
چکیده
We consider an initialand Dirichlet boundaryvalue 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 fourthorder 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 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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