Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

• Published in: Numerische Mathematik Vol. 149; no. 3; pp. 549 - 593
• Main Authors: Filbet, Francis, Rodrigues, L. Miguel, Zakerzadeh, Hamed
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2021; Springer Nature B.V; Springer Verlag
• Subjects: Asymptotic properties; Convergence; Discretization; Larmor radius; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Particle in cell technique; Plasma frequencies; Plasmas (physics); Simulation; Stiffness; Theoretical; Vlasov equations; 65M15; 65L04; 82D10; 35Q83; 65M75; Vlasov-Poisson system; High-order time discretization; Asymptotic preserving schemes; Homogeneous magnetic field; Particle methods
• ISSN: 0029-599X; 0945-3245
• DOI: 10.1007/s00211-021-01248-x

The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes (Filbet and Rodrigues in SIAM J. Numer. Anal. 54(2):1120–1146, 2016) for the Vlasov equation with a strong external magnetic field. In this regime, classical Particle-in-Cell methods are subject to quite restrictive stability constraints on the time and space steps, due to the small Larmor radius and plasma frequency. The asymptotic preserving discretization that we are going to study removes such a constraint while capturing the large-scale dynamics, even when the discretization (in time and space) is too coarse to capture fastest scales. Our error bounds are explicit regarding the discretization, stiffness parameter, initial data and time.