Embedded-Hybridized Discontinuous Galerkin for Magnetohydrodynamics
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This talk introduces a divergence-free and H(div)-conforming Embedded-Hybridized Discontinuous Galerkin discretization for solving the stationary incompressible visco-resistive magnetohydrodynamic (MHD) equations. The EHDG method is computationally cheaper than the corresponding HDG counterpart, with even more significant benefits in the three-dimensional scenario. Furthermore, a specific choice of approximation spaces guarantees that the proposed method is H(div)-conforming, meaning that the velocity and magnetic fields are pointwise divergence-free. We implement our approach in the open-source library MFEM and validate it using manufactured solutions and benchmark test cases. The results indicate that the convergence rates in the L^2 norm for the velocity and magnetic fields are optimal, and the divergence error can be reduced to machine precision. Moreover, the proposed EHDG discretization is pressure-robust.