Abstract: This talk will present the optimal a priori error estimates for the local discontinuous Galerkin methods in one-dimensional mesh and two-dimensional Cartesian mesh, respectively, to solve the time-dependent convection diffusion equations. If the used numerical fluxes for the prime variable and auxiliary variables are of generalized alternating, not purely alternating, there is a one-order and/or one-half-order gap between the existing error estimate and the numerical perform in the L2-norm. By aid of the generalized Gauss-Radau projection and its extension, we are able to fill in the above gap and obtain the optimal error estimates in this status, even though the parameters are not the same in the numerical ux with respect to the prime variable. Finally, some numerical experiments are also given.
