We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a mixed magnetic advection-diffusion problem within a more general Friedrichs system framework. With carefully constructed numerical traces, we introduce two distinct stabilization parameters: $\tau_t$ for the tangential trace and $\tau_n$ for the normal trace. These parameters are tailored to satisfy different requirements, ensuring the stability and convergence of the method. Furthermore, we incorporate a weight function to facilitate the establishment of stability conditions. We also investigate an elementwise postprocessing technique that proves to be effective for both two-dimensional and three-dimensional problems in terms of broken $H({\rm curl})$ semi-norm accuracy improvement. Extensive numerical examples are presented to showcase the performance and effectiveness of the HDG method and the postprocessing techniques.

翻译：我们提出并分析了一种混合化间断伽辽金（HDG）方法，用于在更一般的弗里德里希斯系统框架下求解混合磁对流-扩散问题。通过精心构造数值迹，我们引入了两个不同的稳定化参数：用于切向迹的 $\tau_t$ 和用于法向迹的 $\tau_n$。这些参数针对不同需求设计，确保了方法的稳定性和收敛性。此外，我们引入一个权重函数以方便建立稳定性条件。我们还研究了一种单元级后处理技术，该技术对于二维和三维问题在间断 $H({\rm curl})$ 半范数精度提升方面表现出有效性。大量数值算例展示了HDG方法及后处理技术的性能与有效性。