Local-in-time structure-preserving finite-element schemes for the Euler-Poisson equations

We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling, respectively. 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.