| Abstract: |
| In this talk we introduce an hybridizable DG method for the stationary Magnetohydrodynamics (MHD)
equations with two types of boundary (or constraint) conditions. The method can be hybridized so that the global computational cost is significantly reduced comparing with traditional DG methods. In addition, the method provides exactly divergence-free velocity field. In contrast, the magnetic field is weakly div-free. We provide a priori error estimates for the method on the nonlinear MHD equations. In the smooth case, we have optimal convergence rate for the velocity, magnetic field and pressure in the energy norm, the Lagrange multiplier only has suboptimal convergence order. With the minimal regularity assumption on the exact solution, the approximation is
optimal for all unknowns. To the best of our knowledge, this is the first a priori error estimates of HDG methods for
nonlinear MHD equations. |
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