We devise and analyze a class of the primal discontinuous Galerkin methods for the magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we find a new mechanism under the vector case that provides more flexibility in constructing the schemes. For the more general Friedrichs system, we show the stability and optimal error estimate, which boil down to two core ingredients -- the weight function and the special projection -- that contain information of advection. Numerical experiments are provided to verify the theoretical results.

翻译：我们根据加权后继法,设计并分析一组最初不连续的Galerkin方法,用于处理磁平反扩散问题。除了上风稳定外,我们还在矢量个案下找到一种新机制,为构建计划提供更大的灵活性。对于更普遍的Friedrichs系统,我们展示了稳定性和最佳误差估计,归结为两个核心成分 -- -- 重量函数和特别预测 -- -- 包括平流信息。提供了数值实验,以核实理论结果。