We study the cosmological evolution of domain wall networks in two and three spatial dimensions in the radiation and matter eras using a large number of high-resolution field theory simulations with a large dynamical range. We investigate the dependence of the uncertainty in key parameters characterising the evolution of the network on the size, dynamical range and number of spatial dimensions of the simulations and show that the analytic prediction compares well with the simulation results. We find that there is ample evidence from the simulations of a slow approach of domain wall networks towards a linear scaling solution. However, while at early times the uncertainty in the value of the scaling exponent is small enough for deviations from the scaling solution to be measured, at late times the error bars are much larger and no strong deviations from the scaling solution are found.
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