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A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems

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Abstract

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 \({\varvec{H}}(\textrm{curl})\) semi-norm accuracy improvement. Extensive numerical examples are presented to showcase the performance and effectiveness of the HDG method and the postprocessing techniques.

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The work of Shuonan Wu is supported in part by the Beijing Natural Science Foundation No. 1232007 and the National Natural Science Foundation of China grant No. 12222101.

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Wang, J., Wu, S. A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems. J Sci Comput 99, 86 (2024). https://doi.org/10.1007/s10915-024-02540-2

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