A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains.

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.