Convergence of hp-Streamline Diffusion Method for Vlasov–Maxwell System. Issue 7 (10th November 2019)

• Record Type: Journal Article
• Authors: Asadzadeh, M.; Kowalczyk, P.; Standar, C.
• Is Part Of: Journal of computational and theoretical transport. Volume 48:Issue 7(2019)
• Page Start: 263
• Page End: 279
• Publication Date: 2019-11-10
• Subjects: Vlasov–Maxwell -- stability -- convergence -- hp method; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2019.1694542
• Languages: English
• ISSNs: 2332-4309

Abstract

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 Ω x ⊂ R 3 and velocities v ∈ Ω v ⊂ R 3 . The objective is to show globally optimal a priori error bound of order O ( h / p ) s + 1 / 2, for the SD approximation of the VM system; where h ( = max K h K ) is the mesh size and p ( = max K p K ) 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 H s + 1 ( Ω ) . Numerical implementations, performed for examples in one space- and two velocity dimensions, are justifying the robustness of the theoretical results.