Analysis of a Mixed Discontinuous Galerkin method for incompressible magnetohydrodynamics
报告摘要：We propose and analyze a mixed DG method for the stationary Magnetohydrodynamics (MHD) equations with two types of boundary (or constraint) conditions. The numerical scheme is based a recent work proposed by Houston et. al. for the linearized MHD. With two novel discrete Sobolev embedding type estimates for the discontinuous polynomials, 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 DG methods for nonlinear MHD equations.
20170511Weifeng Qiu Analysis of a Mixed Discontinuous Galerkin method for incompressible magnetohydrodynamics