$f(t,x,y)$ is a solution from NDSolve, in a domain $mathcal{D}$.

If $f(t,x,y)$ was an analytical func I would

$$overline{f(t)}=frac{ int _{mathcal{D}} f(t,x,y) dx dy}{mathcal{D}}$$

Since $f(t,x,y)$ is number for each x point, how can one compute its average value in the domain for a certain $t=t’$? It is basically taking the mean of $f(t’,x,y)$ in the domain but I couldn’t figure out how to do it.