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Using the standard finite element method (FEM) to solve general partialdifferential 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 numericalexperiments is proposed to determine the coefficient of proportionality and$\beta_{\rm R}$ in various space dimensions and FEM packages. Using thecoefficients obtained above, the strategy put forward in \cite{liu386balancing}for predicting the highest achievable accuracy $E_{\rm min}$ and the associatedoptimal number of DoFs $N_{\rm opt}$ for specific problems is extended togeneral problems. This strategy allows predicting $E_{\rm min}$ accurately forgeneral problems, with the CPU time for obtaining the solution with the highestaccuracy $E_{\rm min}$ typically reduced by 60\%--90\%.

A practical algorithm to minimize the overall error in FEM computations