Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov--Poisson Equations

Abstract

A rigorous convergence analysis of the Strang splitting algorithm with a discontinuous Galerkin approximation in space for the Vlasov--Poisson equations is provided. It is shown that under suitable assumptions the error is of order $\mathcal{O}(\tau^2+h^q +h^q/\tau)$, where $\tau$ is the size of a time step, $h$ is the cell size, and $q$ the order of the discontinuous Galerkin approximation. In order to investigate the recurrence phenomena for approximations of higher order as well as to compare the algorithm with numerical results already available in the literature a number of numerical simulations are performed.

Keywords

  1. Strang splitting
  2. discontinuous Galerkin approximation
  3. convergence analysis
  4. Vlasov--Poisson equations
  5. recurrence

MSC codes

  1. 65M12
  2. 82D10
  3. 65L05
  4. 65M60

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Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 757 - 778
ISSN (online): 1095-7170

History

Submitted: 12 November 2012
Accepted: 28 January 2014
Published online: 1 April 2014

Keywords

  1. Strang splitting
  2. discontinuous Galerkin approximation
  3. convergence analysis
  4. Vlasov--Poisson equations
  5. recurrence

MSC codes

  1. 65M12
  2. 82D10
  3. 65L05
  4. 65M60

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