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Robust Finite Elements for linearized Magnetohydrodynamics

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arxiv 2306.15478 v2 pith:M332G3LE submitted 2023-06-27 math.NA cs.NA

L. Beirão da Veiga , F. Dassi , G. Vacca This is my paper · ORCID
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keywords finitefluidlinearizedmagneticmagnetohydrodynamicsmethodrobustterms
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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 $H^1$-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.

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  1. A robust finite element method for linearized magnetohydrodynamics on general domains

    math.NA 2025-06 conditional novelty 6.0 of 10

    A stabilized H(div)/H(curl) finite element scheme extends robust linearized MHD discretizations from convex to general non-convex domains with less regular solutions.

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