Robust H(curl)-based finite element methods for the incompressible MHD system
Abstract
We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on -conforming discretizations for both the velocity and the magnetic field. This choice is guided by the aim of developing methods that are also suitable for the types of solutions arising in problems posed on nonconvex domains. Within this framework, we introduce three stabilized formulations, and study how the stabilization mechanisms employed influence their structural properties. In particular, we focus on suitability for nonconvex polyhedral domains, the need for Lagrange multipliers for the magnetic field, pressure-robustness, and quasi-robustness with respect to both the fluid and magnetic Reynolds numbers. The proposed formulations are further assessed through numerical experiments, highlighting their practical performance.
Cite
@article{arxiv.2604.05717,
title = {Robust H(curl)-based finite element methods for the incompressible MHD system},
author = {Lourenço Beirão da Veiga and Sergio Gómez and Ilaria Perugia and Enrico Zampa},
journal= {arXiv preprint arXiv:2604.05717},
year = {2026}
}