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We formulate an initial- and Dirichlet boundary- value problem for a linearstochastic heat equation, in one space dimension, forced by an additivespace-time white noise. First, we approximate the mild solution to the problemby the solution of the regularized second-order linear stochastic parabolicproblem with random forcing proposed by Allen, Novosel and Zhang (StochasticsStochastics Rep., 64, 1998). Then, we construct numerical approximations of thesolution to the regularized problem by combining the Crank-Nicolson method intime with a standard Galerkin finite element method in space. We derive stronga priori estimates of the modeling error made in approximating the mildsolution to the problem by the solution to the regularized problem, and of thenumerical approximation error of the Crank-Nicolson finite element method.

Crank-Nicolson finite element approximations for a linear stochastic heat equation with additive space-time white noise