L∞L∞ error estimates of discontinuous Galerkin methods for delay differential equations

In this paper, we investigate the convergence behavior of discontinuous Galerkin methods for solving a class of delay differential equations. Although discontinuities may occur in various orders of the derivative of the solutions, we show that the m  -degree DG solutions have (m+1)(m+1)th order accuracy in L∞L∞ norm. Numerical experiments confirm the theoretical results of the methods.