Robust Finite Elements for linearized Magnetohydrodynamics

Understand

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.