Discretization of QFT via Finite Volume method

When working with discretized QFT one moslty works with the Finite Difference Method (FDM) on the hypercubic lattice, and the fields live on sites, links, faces … of the lattice. Also QFT can be defined on non-square domain, like honeycomb lattice, which resembles more the Finite Elements Model (FEM).

And I wonder, whether one has considered a Finite Volumes (https://en.wikipedia.org/wiki/Finite_volume_method) discretization of QFT?

These methods originate from the numerical methods of solving a differential equation, and the latter method actually corresponds to the integration of the equation being solved along a certain domain.
For some conservation law problem, the equation reads:
$$
frac{partial mathbf u}{partial t} + nabla cdot mathbf f(mathbf u) = 0
$$
And the equivalent result in the integral form, after application of the Gauss law:
$$
frac{d bar{mathbf u}_i}{d t} + frac{1}{v_i} oint_{S_i} cdot mathbf f(mathbf u) cdot mathbf n dS = 0
$$
Here we have integrated the first equation over some cell $i$.

Is there some discrete formulation of QFT, where the fields are defined on the cells, and with fluxes, interpolating between the cells? In particular, It would be interesting to think about the fermion discretization.