Abstract
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 and velocities The objective is to show globally optimal a priori error bound of order for the SD approximation of the VM system; where is the mesh size and 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 Numerical implementations, performed for examples in one space- and two velocity dimensions, are justifying the robustness of the theoretical results.
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