In this paper, we present a superconvergence result for the bi-k degree timespace
fully discontinuous finite element of first-order hyperbolic problems. Based on
the element orthogonality analysis (EOA), we first obtain the optimal convergence order
of discontinuous Galerkin finite element solution. Then we use orthogonality correction
technique to prove a superconvergence result at right Radau points, which is
higher one order than the optimal convergence rate. Finally, numerical results are presented
to illustrate the theoretical analysis.