How is the (dis)charging process of capacitors in series calculated?
You can replace the series capacitors with their equivalent total capacitance and then determine the voltage across and current through this equivalent capacitance as a function of time, just as you would if the capacitors where in fact the single equivalent capacitance.

Since the capacitors are in series you know that the current through them must be exactly the same. This means that the change in the total charge must be the same for each capacitor. So the change in voltage for each capacitor must be equal to that change in total charge divided by the individual capacitances. Basically, if you know the current and the capacitance values then you know the voltage.