We generalize and improve the finite element method for linearized Magnetohydrodynamics introduced in (Beirão da Veiga et al., SIAM J. Numer. Anal. 62(4):1539–1564 (2024)). The main novelty is that the proposed scheme is able to handle also non-convex domains and less regular solutions. The method is proved to be pressure robust and quasi-robust with respect to both fluid and magnetic Reynolds numbers. A set of numerical tests confirms our theoretical findings.
Beirão Da Veiga, L., Lovadina, C., Trezzi, M. (2026). A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains. JOURNAL OF SCIENTIFIC COMPUTING, 107(2) [10.1007/s10915-026-03291-y].
A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains
Beirão da Veiga, L.;Trezzi, M.
2026
Abstract
We generalize and improve the finite element method for linearized Magnetohydrodynamics introduced in (Beirão da Veiga et al., SIAM J. Numer. Anal. 62(4):1539–1564 (2024)). The main novelty is that the proposed scheme is able to handle also non-convex domains and less regular solutions. The method is proved to be pressure robust and quasi-robust with respect to both fluid and magnetic Reynolds numbers. A set of numerical tests confirms our theoretical findings.
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