The stability and error analysis of the implicit fully discrete local discontinuous Galerkin method for convection diffusion equations are studied.The fully discrete LDG format is obtained by combining the third-order level implicit Runge-Kutta time discretization and the LDG method with generalized alternating numerical flux.Based on the generalized alternating numerical flux,the relationship between the inner product of the numerical solution and the auxiliary solution is established,and the unconditional stability of the fully discrete local discontinuous Galerkin format is demonstrated.At the same time,the generalized Gauss-Radau projection is introduced,and the optimal error estimate is established by the approximation properties of the projection and some basic inequalities,and finally the correctness of the theoretical analysis of the method is verified by numerical experiments.
维普
万方数据