Superconvergence of discontinuous Galerkin methods for hyperbolic systems

In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h²)$O\left(h^2\right)$-order superconvergence error estimate is established under the conditions of almost uniform partition and the H³$H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Finally, as an application, the numerical treatment of Maxwell equation is discussed and computational results are presented.