Structure-preserving Finite Element Methods for Stationary MHD Models

2015/03/20 by Kaibo Hu, Jinchao Xu, Hu, Kaibo +1 · 1 citation
Engineering · #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1503.06160

openalex publication_date 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop a class of mixed finite element scheme for stationary magnetohydrodynamics (MHD) models, using magnetic field \bm B and current density \bm j as the discretization variables. We show that the Gauss's law for the magnetic field, namely ∇⋅\bmB=0, and the energy law for the entire system are exactly preserved in the finite element schemes. Based on some new basic estimates for H^h(div), we show that the new finite element scheme is well-posed. Furthermore, we show the existence of solutions to the nonlinear problems and the convergence of Picard iterations and finite element methods under some conditions.

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