In Section 3.1 of the 2017 ASPECT paper

`Heister, T., Dannberg, J., Gassmöller, R., Bangerth, W., 2017. High accuracy mantle convection simulation through modern numerical methods. II: Realistic models and problems. Geophys. J. Int. 210 (2), 833–851.`

the CFL constraint has the degree of the polynomial p_T that is used to discretize the temperature in it:

```
∆t ≤ min_K C h_K / ( p_T || u ||_{L_∞} (K) )
```

where C is the CFL number and K is the cell index. My understanding (guess) is that this came about because in the (2012) paper it was written that C defined by

```
CFL_K = ∆t_n ||u||_{∞,K} / h_K ≤ C
```

and experimentally it was found that good values of C were

```
C = 1 / (5.91 p)
```

in 2D and

```
C = 1 / (43.61 p)
```

in 3-D, where p is the polynomial degree with which the temperature variable is discretized.

Is this correct?

Is there any more insight into why the degree of the polynomial p or p_T is needed to maintain stability?