发表机构
Ruhr-Universität Bochum; Uppsala University（波鸿鲁尔大学; 乌普萨拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于凸限制的二阶保正有限元方法求解Vlasov方程，结合SSP时间积分与散度清理，数值实验验证了精度与稳健性。
AI 中文摘要
本文提出了一种新颖的二阶保正有限元方法，用于求解Vlasov方程，该方法采用凸限制算法。该方法使用强稳定性保持（SSP）Runge-Kutta时间积分和相空间网格的张量积构造，以实现高效的高维实现。凸限制算法将稳健的一阶保正图粘性方法与高阶残差基粘性稳定化相结合，从而获得高阶保正格式。本文还提出了适用于高维问题（如Vlasov系统）的新颖一阶和高阶方法。此外，我们提出了一种用于Maxwell方程的散度清理技术，以确保电磁场的散度约束得到满足。数值实验证明了所提方法的准确性和稳健性。
英文摘要
In this paper, we introduce a novel second-order, positivity-preserving finite element method for the Vlasov equations using a convex limiting algorithm. The method employs strong-stability-preserving (SSP) Runge-Kutta time integration and a tensor-product construction of the phase-space mesh for efficient high-dimensional implementations. The convex limiting algorithm combines the robust first-order positivity-preserving graph viscosity approach with high-order residual-based viscosity stabilization to obtain a high-order positivity-preserving scheme. Both novel first-order and high-order methods applicable to high-dimensional problems such as the Vlasov system are presented. In addition, we propose a divergence-cleaning technique for Maxwell's equations to ensure that the divergence constraints of the electromagnetic fields are satisfied. Numerical experiments are provided to demonstrate the accuracy and robustness of the proposed methods.
