Error estimate of high order Runge–Kutta local discontinuous Galerkin method for nonlinear convection-dominated Sobolev equation

In this paper we consider an efficient fully-discrete scheme for solving the nonlinear convection-dominated Sobolev equation, which adopts the local discontinuous Galerkin method with generalized numerical fluxes and high order explicit Runge–Kutta time-marching. By the generalized Gauss-Radau projection and the matrix transferring process, we obtain the optimal L 2 -norm error estimate in both space and time. It is worth mentioning that the bounding constant in error estimate is independent of the reciprocals of diffusion and dispersion coefficients. Finally, numerical experiments are presented to support theoretical results. • A high order, efficient RKLDG scheme based on space–time derivative conversion. • A uniformly optimal L 2 error estimate in space and time. • New energy analysis based on matrix transferring process within LDG framework.