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We introduce a new hybridized discontinuous Galerkin method for theincompressible magnetohydrodynamics equations. If particular velocity,pressure, magnetic field, and magnetic pressure spaces are employed for bothelement and trace solution fields, we arrive at an energy stable method whichreturns pointwise divergence-free velocity fields and magnetic fields andproperly balances linear momentum. We discretize in time using asecond-order-in-time generalized-$\alpha$ method, and we present a blockiterative method for solving the resulting nonlinear system of equations ateach time step. We numerically examine the effectiveness of our method using amanufactured solution and observe our method yields optimal convergence ratesin the $L_2$ norm for the velocity field, pressure field, magnetic field, andmagnetic pressure field. We further find our method is pressure robust. We thenapply our method to a selection of benchmark problems and numerically confirmour method is energy stable.

A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Magnetohydrodynamics Equations