Abstract: We construct a Runge-Kutta discontinuous Galerkin (RKDG) finite element method for two-dimensional compressible gas dynamic equations in Lagrangian coordinate.The equations for fluid dynamics and geometry conservation laws are solved simultaneously.All calculations can be done on fixed meshes.Information of grid velocities are not needed in calculation.Several numerical examples are used to evaluate efficiency and reliability of the scheme.It shows that the algorithm works well.

Key words: Lagrangian coordinate, RKDG finite element method, two-dimensional gas dynamic equations