An anisotropic nonlinear stabilization for finite element approximation of Vlasov-Poisson equations

2025/03/10 by Junjie Wen, Murtazo Nazarov, Wen, Junjie +1 · 2 citations
Engineering · Mathematics · #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2503.07785

openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a high-order finite element method for approximating the Vlasov-Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge-Kutta schemes for time discretization. To stabilize the numerical oscillations inherent in the scheme, a new anisotropic nonlinear artificial viscosity method is introduced. Numerical results demonstrate that this method achieves optimal convergence order with respect to both the polynomial space and time integration. The method is validated using classic benchmark problems for the Vlasov-Poisson equations, including Landau damping, two-stream instability, and bump-on-tail instability in a two-dimensional phase space.

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• High fidelity simulations of the multi-species Vlasov-Maxwell system with the Numerical Flow Iteration
• Extending the Numerical Flow Iteration to the multi-species Vlasov-Maxwell system through Hamiltonian Splitting

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