Abstract
This paper develops energy-preserving discontinuous Galerkin (DG) methods for the Vlasov-Ampère (VA) system coupled with the Dougherty-Fokker-Planck (DFP) collision operator. While the classical VA system has been extensively studied, the inclusion of the collision operator introduces new challenges in conserving the total energy of the system. To address this, we design two energy-conserving temporal discretization methods: a second-order explicit scheme and a second-order implicit-explicit (IMEX) scheme. These schemes are coupled with the DG method, specifically using the local DG (LDG) method for the DFP part. We prove that the fully discrete schemes conserve the total particle number and total energy of the VA-DFP system at the fully discrete level. We further establish the L2 stability of the fully discrete explicit scheme. Numerical experiments are conducted to assess the accuracy, conservation property, and performance of the proposed schemes.
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