2019/03/18 by Eero Hirvijoki, Hirvijoki, Eero
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Numerical methods in engineering #Plasma Physics (physics.plasm-ph)
paper · pdf · doi:10.48550/arxiv.1903.07403
openalex publication_date 2019/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This research note documents new developments regarding finite-element\ndiscretizations of the relativistic Beliaev-Budker Coulomb collision operator\nand the nonrelativistic Landau operator. Where energy conservation in a\nfinite-element approximation of the relativistic collision operator was\npreviously thought to be elusive, it is now achieved even with linear elements.\nThe same result applies to the nonrelativistic Landau operator for which the\nenergy conservation was thought to require at least quadratic elements. In both\ncases, the momentum and density conservation are guaranteed as previously. The\nnew outcomes benefit from the findings reported in a recent\nfinite-difference-scheme paper [Shiroto & Sentoku, arXiv:1902.07866] which we\ngeneralize to the finite-element method. This note focuses solely on the direct\ndiscretization of the collision operator, leaving the discretization of the\nunderlying metriplectic formulation of the relativistic collision operator to\nfuture publications.\n