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 H1-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.
BEIRAO DA VEIGA, L., Dassi, F., Vacca, G. (2024). Robust Finite Elements for Linearized Magnetohydrodynamics. SIAM JOURNAL ON NUMERICAL ANALYSIS, 62(4 (August 31, 2024)), 1539-1564 [10.1137/23m1582783].
Robust Finite Elements for Linearized Magnetohydrodynamics
Lourenco Beirao da Veiga
;Franco Dassi;
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 H1-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.
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