Convergence of hp-Streamline Diffusion Method for Vlasov–Maxwell System
Journal article, 2019

In this paper we study stability and convergence for hp-streamline diffusion (SD) finite element method for the, relativistic, time-dependent Vlasov–Maxwell (VM) system. We consider spatial domain (Formula presented.) and velocities (Formula presented.) The objective is to show globally optimal a priori error bound of order (Formula presented.) for the SD approximation of the VM system; where (Formula presented.) is the mesh size and (Formula presented.) is the spectral order. Our estimates rely on the local version with hK being the diameter of the phase-space-time element K and pK the spectral order for K. The optimal hp estimates require an exact solution in the Sobolev space (Formula presented.) Numerical implementations, performed for examples in one space- and two velocity dimensions, are justifying the robustness of the theoretical results.

convergence

Vlasov–Maxwell

stability

hp method

Author

Mohammad Asadzadeh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

P. Kowalczyk

University of Warsaw, Institute of Applied Mathematics and Mechanics

Christoffer Standar

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational and Theoretical Transport

2332-4309 (ISSN) 2332-4325 (eISSN)

Vol. 48 7 263-279

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.1080/23324309.2019.1694542

More information

Latest update

4/23/2020