Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation

We study the superconvergence property of the local discontinuous Galerkin (LDG) method for solving the linearized Korteweg-de Vries (KdV) equation. We prove that, if the piecewise Pk polynomials with k≥1 are used, the LDG solution converges to a particular projection of the exact solution with the order k+3/2, when the upwind flux is used for the convection term and the alternating flux is used for the dispersive term. Numerical examples are provided at the end to support the theoretical results.