论文标题
磁性对流扩散问题的不连续的盖金方法
Discontinuous Galerkin methods for magnetic advection-diffusion problems
论文作者
论文摘要
我们根据加权方法来设计和分析一类原始不连续的盖尔金方法，用于磁对流扩散问题。除了向上稳定外，我们还在矢量案例下找到了一种新机制，该机制在构建方案方面提供了更大的灵活性。对于更通用的Friedrichs系统，我们显示了稳定性和最佳误差估计，归结于两个核心成分（重量函数和特殊投影），其中包含对流信息。提供数值实验以验证理论结果。
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.
