resolution of these would demand a disproportionately high number of time steps.

Whenever the He-flash driven convective zone penetrates into a region of non-vanishing hydrogen abundance, additional energy is released on a short time scale. As long as the hydrogen abundance is smaller than approximately 0.05, the additional energy from the violent hydrogen fusion is negligible, because of the fact that the helium luminosity is the dominant energy source. When the HECZ is advancing to regions with hydrogen abundances higher than about 0.05, the large H abundance in this zone causes a significant increase of the H-burning rate, which drives a further expansion of the convective zone (see Fig. \[fig4\]). The numerical code then has to follow the ensuing H-burning runaway ($\log (L_{\rm H}/L_\odot)
\ga 10$), during which the subsequent expansion of the star may even lead to a cessation of helium burning.

We found that the most appropriate quantity to determine the onset of the H-flash is $$\label{deltaL}
\delta L = \langle L_{\rm nuc}(\Delta t)\rangle/L_{\rm nuc}(t_0),$$ where $L_{\rm nuc}(t_0)$ is the nuclear luminosity as calculated in the solution of the stellar structure equations, and $\langle L_{\rm
nuc}(\Delta
t)\rangle$ is the average nuclear luminosity derived from the chemical changes within 