  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.
