SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1539-1564, August 2024.
Abstract. 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 nonconforming BDM approach with suitable DG terms for the fluid part, combined with an [math]-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.

中文翻译：

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线性磁流体动力学的鲁棒有限元


《SIAM 数值分析杂志》，第 62 卷，第 4 期，第 1539-1564 页，2024 年 8 月。

抽象的。我们为三个空间维度的线性化磁流体动力学方程引入了压力鲁棒有限元方法，该方法在存在高流体和磁雷诺数的情况下也被证明是准鲁棒的。所提出的方案使用非相容 BDM 方法，为流体部分提供合适的 DG 项，并结合磁通量的数学相容选择。该方法还引入了与耦合项相关的特定 CIP 类型稳定性。最后，通过数值实验进一步验证了理论结果。