Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations

Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations

Year:    2023

Author:    Matthias Maier, John N. Shadid, Ignacio Tomas

Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 647–691

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2022-0205

Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 647–691

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    45

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

Author Details

Matthias Maier

John N. Shadid

Ignacio Tomas

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