A hybridizable discontinuous Galerkin method for magnetic advection-diffusion problems

2023/05/31 by Wang, Jindong, Wu, Shuonan · 2 citations
#65N12 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2305.19806

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: τ_t for the tangential trace and τ_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.

Cited by

• A streamline upwind/Petrov-Galerkin method for the magnetic advection-diffusion problem
• Local projection stabilization methods for \boldsymbolH(\rm curl) and \boldsymbolH(\rm div) advection problems

Related

• Discontinuous Galerkin methods for magnetic advection-diffusion problems
• A streamline upwind/Petrov-Galerkin method for the magnetic advection-diffusion problem
• Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations
• A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Magnetohydrodynamics Equations
• A flux-based HDG method