3D local mesh refinement in heated sphere

A sphere is heated from the inside, by a prescribed temperature at the middle.

First a solution is determined on a coarse mesh, then a local mesh refinement is applied. The local mesh refinement automatically takes place at those places where the residue in the equation (the heat equation) is high, which is near the middle of the sphere.

We show residues in the final (refined) mesh:

Here is the Inputfile.