  We discuss structure-preserving numerical discretizations for repulsive and
attractive Euler-Poisson equations that find applications in fluid-plasma and
self-gravitation modeling. The scheme is fully discrete and structure
preserving in the sense that it maintains a discrete energy law, as well as
hyperbolic invariant domain properties, such as positivity of the density and a
minimum principle of the specific entropy. A detailed discussion of algorithmic
details is given, as well as proofs of the claimed properties. We present
computational experiments corroborating our analytical findings and
demonstrating the computational capabilities of the scheme.

Numerical Analysis;Numerical Analysis;Computational Physics