A sphere has zero temperature at the outer surface, and contains a heat source in the middle such that the temperature in the middle is 1. The temperature distribution is calculated. A wire frame plot of the initial mesh (with -TET4 elements) is given below
Using the local refinement algorithm, 10 percent of the elements are refined after the time stepping shown in the figure. The residue in the temperature equation is used to select which elements need to be refined. Since the residue in the temperature equation is most large near the heat source in the middle, the local refinement algorithm places most elements near the middle. This can be seen in the wire frame plot below
