  Generalizing an idea of Davie and Gaines (2001), we present a method for the
simulation of fully discrete samples of the solution to the stochastic heat
equation on an interval. We provide a condition for the validity of the
approximation, which holds particularly when the number of temporal and spatial
observations tends to infinity. Hereby, the quality of the approximation is
measured in total variation distance. In a simulation study we calculate
temporal and spatial quadratic variations from sample paths generated both via
our method and via naive truncation of the Fourier series representation of the
process. Hereby, the results provided by our method are more accurate at a
considerably lower computational cost.
