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.
Keywords: Euler-Poisson equations; operator splitting; invariant domain preservation; discrete energy balance.