I did similar to @DentdeLion. A computation using {t, 0, .001*tfin} took a few seconds and brought me to MaxMemoryUsed[] of 434 Mb. I then upped it to .01*tfin.

In[690]:= AbsoluteTiming[
 uifwave = 
  NDSolveValue[{op == 0, dirc, ic, dic}, \[Eta][t, x, y], {t, 
    0, .01*tfin}, {x, y} \[Element] mesh]]

Out[690]= {65.8217, 
 InterpolatingFunction[{{0., 53.5719}, {0., 70.}, {0., 94.5}}, <>][t, 
  x, y]}

In[691]:= MaxMemoryUsed[]

Out[691]= 1084091256 

Extrapolating from that suggests the full computation really takes more memory than most Mathematica kernels will have available.

It seems likely that mesh was not defined when you executed NDSolveValue. That is what the error message shows. Since mesh is defined in another cell, it somehow became undefined. If it was not an action on your part (even an accidental one), then perhaps the kernel crashed. It possibly could be from running out of memory. NDSolve is taking up several gigabytes right now, and I might not let it run to completion.