Computational and Applied Mathematics seminar

Abstract:
We show improved convergence for a $h-p$, streamline diffusion (SD), Nitsche's scheme for the Vlasov-Maxwell (VM) system. The standard Galerkin for VM equations, as 1st order hyperbolic, suffers from the draw-back of poor convergence. We have improved this convergence rate using:

(i) The SD method that adds artificial diffusion to the system.

(ii) The $h-p$ approach to gain adaptivity feature.

(iii) Combined, differentiated, Maxwell equations to render the first order hyperbolic system to a second order hyperbolic equation (not applicable to Vlasov part).

(iv) Add of {\sl symmetry} and {\sl penalty} terms to reach final step of Nitsche's scheme.

Numerical examples are justifying the theory.