Abstract: We combine Runge-Kutta discontinuous finite element method(RKDG) with adaptive method to solve Euler equations.Domain is divided into unstructured tetrahedral meshes.Local mesh refinement technique is used.According to changes in numerical solution,mesh is refined or coarsened locally.Therefore,number of overall grids is reduced and computational efficiency is increased.We give four different adaptive strategies and analyze advantages and disadvantages.Finally,several examples validate the method.

Key words: discontinuous finite element method, adaptive method, hyperbolic conservation law