Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws

Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…