# Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations

## TL;DR

This paper introduces a hybridized discontinuous Galerkin method for stationary linearized incompressible MHD equations, providing error estimates and numerical verification of optimal convergence in multiple dimensions.

## Contribution

It develops a novel HDG flux formulation for MHD equations enabling hybridization and derives rigorous error estimates with numerical validation.

## Key findings

- Optimal convergence for fluid velocity and magnetic variables
- Quasi-optimal convergence for other quantities
- Numerical results confirm theoretical error estimates

## Abstract

We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduction of an HDG flux of the dual saddle-point form of the MHD equations that facilitates the hybridization of discontinuous Galerkin (DG) method. We carry out the $\textit{a priori}$ error estimates for the proposed HDG method on simplicial meshes in both two- and three-dimensions. The analysis provides optimal convergence for the fluid velocity and the magnetic variables, and quasi-optimal convergence for the remaining quantities. Numerical examples are presented to verify the theoretical findings.