  The Active Flux scheme is a finite volume scheme with additional point values
distributed along the cell boundary. It is third order accurate and does not
require a Riemann solver. Instead, given a reconstruction, the initial value
problem at the location of the point value is solved. The intercell flux is
then obtained from the evolved values along the cell boundary by quadrature.
Whereas for linear problems an exact evolution operator is available, for
nonlinear problems one needs to resort to approximate evolution operators. This
paper presents such approximate operators for nonlinear hyperbolic systems in
one dimension and nonlinear scalar equations in multiple spatial dimensions.
They are obtained by estimating the wave speeds to sufficient order of
accuracy. Additionally, an entropy fix is introduced and a new limiting
strategy is proposed. The abilities of the scheme are assessed on a variety of
smooth and discontinuous setups.
