We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a non-conforming BDM approach with suitable DG terms for the fluid part, combined with an $H^1$-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments.

翻译：我们针对三维空间中线性化磁流体动力学方程组，提出了一种压力鲁棒有限元方法。该方法在流体和磁雷诺数较高时，被证明具有准鲁棒性。所提方案对流体部分采用非协调BDM方法，配合合适的DG项，同时对磁通量采用$H^1$协调选择。该方法还引入了一种与耦合项相关的特定CIP型稳定化。最后，通过数值实验进一步验证了理论结果。