报告人：石珂 (Old Dominion University)

时间：2017年3月6日9:00 - 10：00

地点：华中科技大学恩明楼813

题目: A Mixed Discontinuous Galerkin method for incompressible magnetohydrodynamics

摘要：

In this talk we propose and analyze a mixed DG method for the stationary Magnetohydrodynamics (MHD) equations. The numerical scheme is based a recent work proposed by Houston et. al. for the linearized MHD. With a novel discrete Sobolev embedding type estimate 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. We will present a novel $L^3$-norm estimate for discrete polynomials which plays a key rule in the analysis.