X1 = 0.0;
Y1 = 0.0;
Z1 = 0.0;
X2 = 1.0;
Y2 = 8.0;
Z2 = 1.0;
Ymid = 0.5 (Y2 + Y1);
aDim = 0.5;
reg1=Rectangle[{X1,Y1},{X2,Y2}];
reg2=Triangle[{{X1,Ymid+COD},{X1,Ymid-COD},{aDim,Ymid}}];
reg3=RegionDifference[reg1,reg2];
reg4=RegionProduct[reg3,Line[{{Z1},{Z2}}]];
elVol =5(Subscript[[ScriptL], 0]/2)^3/(6[Sqrt]2);
MeshIn = ToElementMesh[reg4, MaxCellMeasure -> {"Volume" -> 0.0125},
"MeshOrder" -> 1,
MeshRefinementFunction ->
Function[{vertices, Vol},
Block[{x, y, z, tol}, {x, y, z} = Mean[vertices]; tol = 0.05;
If[y < Ymid + tol && y > Ymid - tol && x > aDim - tol ,
 Vol > elVol, Vol > 5]]]]

f[x_,y_,z_] = x y^2 + z^2;

NIntegrate[f[x,y,z],{y,0,8},{z,0,1}];

NIntegrate[f[x,y,z], {x, y, z} [Element] meshIn]