Convergence of hp-Streamline Diffusion Method for Vlasov–Maxwell System
Artikel i vetenskaplig tidskrift, 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

stability

hp method

Vlasov–Maxwell

Författare

Mohammad Asadzadeh

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

P. Kowalczyk

University of Warsaw, Institute of Applied Mathematics and Mechanics

Christoffer Standar

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Journal of Computational and Theoretical Transport

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

Vol. in press

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Signalbehandling

DOI

10.1080/23324309.2019.1694542

Mer information

Senast uppdaterat

2019-12-10