Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations (Communications in Computational Physics, 2019)
By combining the characteristic method and the local discontinuous Galerkinmethod with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in R2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2−norm of the errors inboth velocity and pressure are derived. Some numerical experiments are performed toverify theoretical results.