  Using the standard finite element method (FEM) to solve general partial
differential equations, the round-off error is found to be proportional to
$N^{\beta_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and
$\beta_{\rm R}$ a coefficient. A method which uses a few cheap numerical
experiments is proposed to determine the coefficient of proportionality and
$\beta_{\rm R}$ in various space dimensions and FEM packages. Using the
coefficients obtained above, the strategy put forward in \cite{liu386balancing}
for predicting the highest achievable accuracy $E_{\rm min}$ and the associated
optimal number of DoFs $N_{\rm opt}$ for specific problems is extended to
general problems. This strategy allows predicting $E_{\rm min}$ accurately for
general problems, with the CPU time for obtaining the solution with the highest
accuracy $E_{\rm min}$ typically reduced by 60\%--90\%.
