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Bibliographic Details
Main Authors: Kormann, Katharina, Nazarov, Murtazo, Wen, Junjie
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.07607
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author Kormann, Katharina
Nazarov, Murtazo
Wen, Junjie
author_facet Kormann, Katharina
Nazarov, Murtazo
Wen, Junjie
contents We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to discretize the Vlasov equation, combined with curl- and divergence-conforming Nédélec and Raviart-Thomas elements for Maxwell's equations on Cartesian grids. A novel, robust, consistent, and high-order accurate residual-based artificial viscosity method is introduced for stabilizing the Vlasov equations. The proposed method is tested on the 1D2V and 2D2V reduced Vlasov-Maxwell system, achieving optimal convergence orders for all polynomial spaces considered in this study. Several challenging benchmarks are solved to validate the effectiveness of the proposed method.
format Preprint
id arxiv_https___arxiv_org_abs_2507_07607
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A structure-preserving finite element framework for the Vlasov-Maxwell system
Kormann, Katharina
Nazarov, Murtazo
Wen, Junjie
Numerical Analysis
We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces for the spatial and velocity domains, respectively, to discretize the Vlasov equation, combined with curl- and divergence-conforming Nédélec and Raviart-Thomas elements for Maxwell's equations on Cartesian grids. A novel, robust, consistent, and high-order accurate residual-based artificial viscosity method is introduced for stabilizing the Vlasov equations. The proposed method is tested on the 1D2V and 2D2V reduced Vlasov-Maxwell system, achieving optimal convergence orders for all polynomial spaces considered in this study. Several challenging benchmarks are solved to validate the effectiveness of the proposed method.
title A structure-preserving finite element framework for the Vlasov-Maxwell system
topic Numerical Analysis
url https://arxiv.org/abs/2507.07607