On the Accuracy of Discontinuous Galerkin Methods in the Time Domain

Abstract

In this paper, the solution accuracy of the time-discontinuous Galerkin (TDG) and bi-discontinuous Galerkin (BDG) methods is studied. It has been shown that the accuracies for TDG and BDG methods are of order 2m — 1 and 2m — 2, respectively, at the end of the time interval. It is found that the accuracy is in general of order m — 1 and m — 2 for TDG and BDG methods, respectively, within the time interval. The discrepancy at the initial time is of the same order of accuracy as the other points within the time interval. It is also found that some points within the time interval are of one-order higher in accuracy. These locations for lower-order interpolations are given. To maintain higher-order accuracy at the end of the time interval, it is shown that the forcing excitation should be accurate up to order 2m — 1 and 2m — 2 for TDG and BDG methods, respectively.