Mesh definition in 3d is size dependent

Question

Can somebody tell me if this is a bug?

<< NDSolve`FEM`
Table[
  x0 = 2.5;
  cords = {{-x0, 0, 0}, {x0, 0, 0}};
  r = 
    RegionDifference[
      Cuboid[{- L, -L, -L}, {L, L, L}], 
      RegionUnion[Ball[#, 1] & /@ cords]];
  mesh2 = ToElementMesh[ r, "RegionHoles" -> cords];
  mesh2["Wireframe"], 
  {L, 4, 10, 2}]

As you can see the holes in the middle loose their shape as the outer cube becomes larger.

I've tried two different ways of fixing the problem: defining a MeshRefinementFunction and using implicit region instead of region unions. Neither work. A similar problem I faced with a previous version of Mathematica in 2D is documented here.

If you look carefully at the documentation you can see the same problem:

The inner ellipse has a really bad resolution even though the elements are quite small.

Running 10.3.1 in macosx 10.8.5

Answer 1

It's not a bug this is what is expected. Here is what I get in 10.4.1

<< NDSolve`FEM`
GraphicsRow[Table[x0 = 2.5;
  cords = {{-x0, 0, 0}, {x0, 0, 0}};
  r = RegionDifference[Cuboid[{-L, -L, -L}, {L, L, L}], 
    RegionUnion[Ball[#, 1] & /@ cords]];
  mesh2 = ToElementMesh[r, "RegionHoles" -> cords];
  mesh2["Wireframe"[PlotRange -> {{-L, L}, {0, L}, {-L, L}}]], {L, 4, 
   10, 2}], ImageSize -> Full]

You can use "MaxBoundaryCellSize" to resolve the smaller features:

<< NDSolve`FEM`
GraphicsRow[Table[x0 = 2.5;
  cords = {{-x0, 0, 0}, {x0, 0, 0}};
  r = RegionDifference[Cuboid[{-L, -L, -L}, {L, L, L}], 
    RegionUnion[Ball[#, 1] & /@ cords]];
  mesh2 = 
   ToElementMesh[r, "RegionHoles" -> cords, 
    "MaxBoundaryCellMeasure" -> 1];
  mesh2["Wireframe"[PlotRange -> {{-L, L}, {0, L}, {-L, L}}]], {L, 4, 
   10, 2}], ImageSize -> Full]