TY - JOUR
T1 - Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations
AU - Maier , Matthias
AU - Shadid , John N.
AU - Tomas , Ignacio
JO - Communications in Computational Physics
VL - 3
SP - 647
EP - 691
PY - 2023
DA - 2023/04
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0205
UR - https://global-sci.org/intro/article_detail/cicp/21656.html
KW - Euler-Poisson equations, operator splitting, invariant domain preservation, discrete energy balance.
AB - <p style="text-align: justify;">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.</p>