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arXiv · 1702.05124

Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations

Jeonghun J. Lee·Stephen Shannon·Tan Bui-Thanh·John N. Shadid
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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.

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Jeonghun J. Lee, Stephen Shannon, Tan Bui-Thanh, John N. Shadid. 2017-02-16. Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations. https://arxiv.org/abs/1702.05124

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