The optimal error estimate and superconvergence of the local discontinuous Galerkin methods for one-dimensional linear fifth order time dependent equations

In this paper, we investigate the optimal error estimate and the superconvergence of linear fifth order time dependent equations. We prove that the local discontinuous Galerkin (LDG) solution is (k+1)(k+1)th order convergent when the piecewise PkPk space is used. Also, the numerical solution is (k+32)th order superconvergent to a particular projection of the exact solution. The numerical experiences indicate that the order of the superconvergence is (k+2)(k+2), which implies the result obtained in this paper is suboptimal.