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hp streamline-diffusion and discontinuous Galekin schemes with Nitsche correction for the three dimensional Vlasov-Maxwell system.

Mohammad Asadzadeh (Institutionen för matematiska vetenskaper, Tillämpad matematik och statistik) ; Piotr Kowalczyk ; Christoffer Standar (Institutionen för matematiska vetenskaper)
(2017)
[Preprint]

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 of order s, we derive global {\sl a priori} error bound of order s+1/2 in h/p, where h is the mesh parameter and p is the spectral order. This estimate is based on the local version with hK= diam K being the diameter of the {\sl phase-space-time} element K and pK 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 {\sl elliptic type} equation. Then, combining the Nitsche's method for the spatial discretization with a second order time scheme, we obtain optimal convergence of (h2+k2), 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 [20].

Nyckelord: hp-method and Streamline Diffusion and Discontinuous Galerkin and Vlasov-Maxwell system and Nitsche scheme.



Denna post skapades 2018-01-03.
CPL Pubid: 254276

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Tillämpad matematik och statistikInstitutionen för matematiska vetenskaper, Tillämpad matematik och statistik (GU)
Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

Ämnesområden

Matematik

Chalmers infrastruktur