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Volume 33, Issue 3
Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations

Matthias Maier, John N. Shadid & Ignacio Tomas

DOI: 10.4208/cicp.OA-2022-0205

Commun. Comput. Phys., 33 (2023), pp. 647-691.

Published online: 2023-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M22, 35L65, 35Q31

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-33-647, author = {Maier , MatthiasShadid , John N. and Tomas , Ignacio}, title = {Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0205}, url = {http://global-sci.org/intro/article_detail/cicp/21656.html} }
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 -

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.

Maier , MatthiasShadid , John N. and Tomas , Ignacio. (2023). Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations. Communications in Computational Physics. 33 (3). 647-691. doi:10.4208/cicp.OA-2022-0205
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