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In this paper, we investigate the superconvergence property of the local discontinuous Galerkin (LDG) methods for solving one-dimensional linear time dependent fourth order problems. We prove that the error between the LDG solution and a particular projection of the exact solution, $\bar{e}_u$, achieves $(k+\frac32)$-th order superconvergence when polynomials of degree $k$ ($k\ge 1$) are used. Numerical experiments of $P^k$ polynomials, with $1\le k \le3$, are displayed to demonstrate the theoretical results, which show that the error $\bar{e}_u$ actually achieves $(k+2)$-th order superconvergence, indicating that the error bound for $\bar{e}_u$ obtained in this paper is sub-optimal. Initial-boundary value problems, nonlinear equations and solutions having singularities are numerically investigated to verify that the conclusions hold true for very general cases.

local discontinuous Galerkin method, superconvergence, fourth order problems, error estimates