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In this paper, high-order Discontinuous Galerkin Methods are used to solve the 2d Euler equations and 2d Navier-Stokes equations.In inviscid cases, A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities.For viscous flows, only the laminar cases are considered here.In order to ensure the stability of the relaxation, a Newton-GMRES method and a Newton-multigrid method are employed.Numerical results indicate that highly accurate solutions can be obtained even on very coarse grids when high order is used.