Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations (Communications in Computational Physics, 2023)
We discuss structure-preserving numerical discretizations for repulsive andattractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in thesense that it maintains a discrete energy law, as well as hyperbolic invariant domainproperties, such as positivity of the density and a minimum principle of the specificentropy. A detailed discussion of algorithmic details is given, as well as proofs of theclaimed properties. We present computational experiments corroborating our analytical findings and demonstrating the computational capabilities of the scheme.