By combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in ℝ
2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L
2–norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.