Some new properties of an Active flux type scheme: PamPa
For numerical analysts and computational scientists, this provides theoretical foundations and new properties for a class of high-order finite volume schemes.
The paper reveals that Active Flux/PamPa schemes incorporate discontinuous Galerkin as a building block, possess intrinsic bound-preserving properties, and satisfy the summation-by-parts property in 1D.
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pampa schemes can be interpreted in such a way that the discontinuous Galerkin (dG) scheme is one of their building blocks. Secondly we provide intrinsic bound preserving properties of the current variant of pampa. This is also illustrated numerically. Last, we show, at least in one dimension, that the pampa scheme has the summation by part (SBP) property.