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：本文针对三维线性化磁流体动力学方程提出了一种压力鲁棒的有限元方法，该方法在流体和磁雷诺数较高的情况下仍可证明具有准鲁棒性。所提出的方案采用非协调BDM方法，并结合流体部分的合适DG项，同时选择$H^1$协调的磁通量形式。该方法还引入了与耦合项相关的特定CIP型稳定化技术。最后，通过数值实验进一步验证了理论结果。