On hp-streamline diffusion and Nitsche schemes for the relativistic Vlasov-Maxwell system
Artikel i vetenskaplig tidskrift, 2019

We study stability and convergence of hp-streamline diffusion (SD) finite element, and Nitsche's schemes for the three dimensional, relativistic (3 spatial dimension and 3 velocities), time dependent Vlasov-Maxwell system and Maxwell's equations, respectively. For the hp scheme for the Vlasov-Maxwell system, assuming that the exact solution is in the Sobolev space HS+1(Omega), we derive global a priori error bound of order O(h/p)(s+1/2), where h(= max(K) h(K)) is the mesh parameter and p(= max(K) p(K)) is the spectral order. This estimate is based on the local version with h(K) = diam K being the diameter of the phase-space-time element K and pR-is the spectral order (the degree of approximating finite element polynomial) for K. As for the Nitsche's scheme, by a simple calculus of the field equations, first we convert the Maxwell's system to an elliptic type equation. Then, combining the Nitsche's method for the spatial discretization with a second order time scheme, we obtain optimal convergence of O(h(2) +k(2)), where h is the spatial mesh size and k is the time step. Here, as in the classical literature, the second order time scheme requires higher order regularity assumptions. Numerical justification of the results, in lower dimensions, is presented and is also the subject of a forthcoming computational work [22].

discontinuous Galerkin

Streamline diffusion

Vlasov-Maxwell system

hp-method

Nitsche scheme

Författare

Mohammad Asadzadeh

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Piotr Kowalczyk

Uniwersytet Warszawski

Christoffer Standar

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Kinetic and Related Models

1937-5093 (ISSN) 1937-5077 (eISSN)

Vol. 12 1 105-131

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.3934/krm.2019005

Mer information

Senast uppdaterat

2018-11-30