it is usually less effective as the diffusion for $\alpha=2$. For that case, we
choose a slightly more readable definition of the viscosity,
@f{eqnarray*}
- \nu_2(T)|_K = \min (\nu_h^\mathrm{max}|_K,\nu_h^\mathrm{E}_K)
+ \nu_2(T)|_K = \min (\nu_h^\mathrm{max}|_K,\nu_h^\mathrm{E}|_K)
@f}
where the first term gives again the maximum dissipation (similarly to a first
order upwind scheme),
@f{eqnarray*}
- \nu^\mathrm{max}_h|_K = \beta h_K \|\ve u\|_{L^\infty}(K)}
+ \nu^\mathrm{max}_h|_K = \beta h_K \|\mathrm u\|_{L^\infty}(K)}
@f}
and the entropy viscosity is defined as
@f{eqnarray*}
minimum temperature in the computation), which gives the following formula
@f{eqnarray*}
R_\mathrm{E}(T) = \frac{\partial E(T)}{\partial t} +
- (T-T_\mathrm{m}) \left(\ve u \cdot \nabla T - \kappa \nabla^2 T - \gamma\right).
+ (T-T_\mathrm{m}) \left(\mathrm u \cdot \nabla T - \kappa \nabla^2 T - \gamma\right).
@f}
The denominator in the formula for $\nu^\mathrm{E}_h|_K$ is computed as the
global deviation of the entropy from the space-averaged entropy $\bar{E}(T) =