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.
A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains / L.B. Da Veiga, C.L.. - In: JOURNAL OF SCIENTIFIC COMPUTING. - ISSN 0885-7474. - 107:2(2026 Apr 11), pp. 73.1-73.30. [10.1007/s10915-026-03291-y]
A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains
C. LovadinaPenultimo
;
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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