Runge-Kutta and Lax-Wendroff Discontinuous Galerkin Methods for Linear Conservation Laws.

In this talk we give a short summary of our recent work [5], jointly with Z. Sun, on establishing the equivalency of the Runge-Kutta discontinuous Galerkin (RKDG) methods and a class of Lax-Wendroff discontinuous Galerkin (LWDG) methods for solving linear conservation laws, as well as on stability analysis and error estimates for the LWDG methods for solving one- and two-dimensional linear conservation laws, regardless of whether they are equivalent to the RKDG methods or not. Our stability analysis includes multidimensional problems with divergence-free coefficients, and our error estimates include those for both the solution u and its first order time derivative u_t. [ABSTRACT FROM AUTHOR]