A robust finite element method for linearized magnetohydrodynamics on general domains

TL;DR

This paper introduces a finite element method for linearized magnetohydrodynamics that effectively handles non-convex domains and irregular solutions, ensuring robustness across various physical parameters.

Contribution

The novel scheme is pressure robust, quasi-robust, and capable of managing complex domain geometries and less regular solutions in magnetohydrodynamics.

Findings

Method handles non-convex domains and irregular solutions.

Proven to be pressure robust and quasi-robust.

Effective across different Reynolds numbers.

Abstract

We propose a new finite element method for linearized Magnetohydrodynamics. 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.