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We investigate two efficient time discretizations for the post-processingtechnique of discontinuous Galerkin (DG) methods to solve hyperbolicconservation laws. The post-processing technique, which is applied at the finaltime of the DG method, can enhance the accuracy of the original DG solution(spatial superconvergence). One main difficulty of the post-processingtechnique is that the spatial superconvergence after post-processing needs tobe matched with proper temporary accuracy. If the semi-discretized system (ODEsystem after spatial discretization) is under-resolved in time, then the spacesuperconvergence will be concealed. In this paper, we focus our investigationon the recently designed SDG method and derive its explicit scheme from acorrection process based on the DG weak formulation. We also introduce anothersimilar technique, namely the spectral deferred correction (SDC) method. Acomparison is made among both proposed time discretization techniques with thestandard third-order Runge-Kutta method through several numerical examples, toconclude that both the SDG and SDC methods are efficient time discretizationtechniques for exploiting the spatial superconvergence of the DG methods.

Efficient Time Discretization for Exploring Spatial Superconvergence of Discontinuous Galerkin Methods