Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system

TL;DR

This paper develops error estimates for a finite element method that preserves key physical invariants like energy and helicities in a magnetohydrodynamics system, ensuring accurate and stable numerical simulations.

Contribution

It introduces a helicity-preserving finite element discretisation for incompressible magnetohydrodynamics and derives rigorous error estimates for this method.

Findings

The method preserves energy, magnetic, and cross helicities at the discrete level.

Error bounds are established for the finite element approximation.

The approach enhances stability and physical fidelity of MHD simulations.

Abstract

We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the discrete level.