When `FiniteElement` method is used, the differential equations will first be transformed to certain _standard form_ (named as formal PDE in recent FEM document), and it turns out to be critical to check what the _standard form_ is when analyzing various issues related to FEM. Here are some examples:

https://mathematica.stackexchange.com/q/131542/1871

https://mathematica.stackexchange.com/q/147089/1871

https://mathematica.stackexchange.com/q/194356/1871

https://mathematica.stackexchange.com/q/198894/1871

The coefficient of formal PDE is available from `PDECoefficientData`, but its output is just hard to read. For example, with

    {state} = NDSolve`ProcessEquations[
                With[{u = u[x, y]}, {-2 D[u, y, y] - 3 D[u, x, x] == 1, 
                                     DirichletCondition[u == 0, True]}], 
                u, {x, 0, 1}, {y, 0, 1}];
    
    data = state["FiniteElementData"]["PDECoefficientData"];
    
    data["All"]
    (* {{{{1}}, {{{{0}, {0}}}}}, {{{{{3, 0}, {0, 2}}}}, {{{{0}, {0}}}}, {{{{0, 
      0}}}}, {{0}}}, {{{0}}}, {{{0}}}} *)

at hand, can you tell what's what? Can you label $d$, $c$, $\alpha$, etc. in the formal PDE

$$d\frac{\partial }{\partial t}u+\nabla \cdot (-c \nabla u-\alpha  u+\gamma ) +\beta \cdot \nabla u+ a u -f=0$$

with corresponding values, without doubt?

Can we have a function that shows the formal PDE of `FiniteElement` in a easy-to-read way? A possible (but not necessary of course) input-output in my mind:

    showFormalPDE@With[{u = u[x, y]}, -2 D[u, y, y] - 3 D[u, x, x] == 1]
    (* -1 + Inactive[Div][(-{{3, 0}, {0, 2}}.Inactive[Grad][u[x, y], {x, y}]), {x, y}] == 0 *)