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