  This work focuses on the numerical solution of hyperbolic conservations laws
(possibly endowed with a source term) using the Active Flux method. This method
is an extension of the finite volume method. Instead of solving a Riemann
Problem, the Active Flux method uses actively evolved point values along the
cell boundary in order to compute the numerical flux. Early applications of the
method were linear equations with an available exact solution operator, and
Active Flux was shown to be structure preserving in such cases. For nonlinear
PDEs or balance laws, exact evolution operators generally are unavailable.
Here, strategies are shown how sufficiently accurate approximate evolution
operators can be designed which allow to make Active Flux structure preserving
/ well-balanced for nonlinear problems.
