Discontinuous Galerkin methods for magnetic advection-diffusion problems

2022/08/02 by Jindong Wang, Shuonan Wu, Wang, Jindong +1 · 1 citation
Engineering · Mathematics · #65N12 #65N60 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2208.01267

openalex publication_date 2022/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Local projection stabilization methods for \boldsymbolH(\rm curl) and \boldsymbolH(\rm div) advection problems

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