Structure-preserving finite-element schemes for the Euler-Poisson equations

TL;DR

This paper introduces a fully discrete finite-element scheme for Euler-Poisson equations that preserves key physical properties like energy and positivity, with proven stability and demonstrated computational effectiveness.

Contribution

It presents a novel structure-preserving finite-element discretization for Euler-Poisson equations that maintains energy laws and invariant domain properties.

Findings

The scheme preserves discrete energy and positivity.

Computational experiments confirm stability and accuracy.

The method is applicable to fluid-plasma and self-gravitation models.

Abstract

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.