Averaged flux

Hi,

how to average the time-dependent diffusive flux for pre-defined time intervals at a domain boundary and allocate those (averaged) values to the arithmetic mean of the time intervals? The evaluation of the averages is part of the computational (not post processing) phase.

Hence, I would like to evaluate the following expression at a given boundary:

Integral flux from t(i) until t(i+1) devided by the length of the time interval ( t(i+1) - t(i) ); that averaged flux value should be allocated to time point ( t(i+1) + t(i) ) /2, i.e. the middle of the time interval.

Many thanks for your appreciated help.

Best regards,

Andreas