The DG-FEM Under Three Slope-limits For Euler Equation

The discontinuous galerkin finite element method(DG-FEM) is a method for Com-putational Fluid Dynamics,appears to have been proposed first in solving the neutron-transport problem,and then this method developed very quickly,and have solved a lot of linearity-problem.Along with the theoretical analysis developed,we found that:the discontinuous galerkin finite element method has high-efficiency,high-accurate character-istic as in solving the problem with discontinuous solution,At the same time,it is high-resolution, cut down the numerical-oscillation,so it is used to solve the non-line problems: convection-diffusion equation,Maxwell equation,shallow water wave equation and so on.In this page,I mainly discuss the gas dynamics—Euler equations,Use the discontinuous finite element for dispersion,subdivision.First,I use R.J.LeVeque,J.W.Thomas's limiter(recorded as∏~1) to make programme and get the numerical solution of Euler equations;Second,I use B.Cockburn's limiter(recorded as∏~2) to make programme and get the numerical solution of Euler equations;Then,I found the new limiter(recorded as∏~3) and I use this new limiter(∏~3) to make programme and get the numerical solution of Euler equations;Last,I compare the results which come from these three methods and found that:For the Euler equations,with the new limiter(∏~3),the result is more accurate, faster convergence rate,especially in solutions containing intermittent Department.