Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations
Numerical Analysis
2019-01-15 v6
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 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.
Keywords
Cite
@article{arxiv.1702.05124,
title = {Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations},
author = {Jeonghun J. Lee and Stephen Shannon and Tan Bui-Thanh and John N. Shadid},
journal= {arXiv preprint arXiv:1702.05124},
year = {2019}
}