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Energy conserving discontinuous Galerkin spectral element method for the Vlasov–Poisson system
- Source :
- Journal of Computational Physics
- Publication Year :
- 2014
- Publisher :
- Elsevier BV, 2014.
-
Abstract
- We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov–Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [4] , with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solving multiple Poisson problems, and all the integrals appearing in the finite element formulation are approximated with Gauss–Lobatto quadrature, thereby yielding a spectral element formulation. The resulting method has the following properties: exact energy conservation (up to errors introduced by the time discretization), stability (thanks to the use of upwind numerical fluxes), high order accuracy and high locality. For the time discretization, we consider both Runge–Kutta methods and exponential integrators, and show results for 1D and 2D cases (2D and 4D in phase space, respectively).
- Subjects :
- Numerical Analysis
Physics and Astronomy (miscellaneous)
Discretization
Applied Mathematics
Mathematical analysis
Spectral element method
Exponential integrator
Finite element method
Computer Science Applications
Quadrature (mathematics)
Computational Mathematics
Discontinuous Galerkin method
Modeling and Simulation
Phase space
Spectral method
Mathematics
Subjects
Details
- ISSN :
- 00219991
- Volume :
- 279
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi.dedup.....d387e131e232c2ef1bc112e7281d5785