Robust Finite Elements for linearized Magnetohydrodynamics

2023/06/27 by da Veiga, L. Beirão, Dassi, F., Vacca, G. · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2306.15478

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 non-conforming 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.

Cited by

• A robust finite element method for linearized magnetohydrodynamics on general domains
• A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows

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