A Fully-Discrete Local Discontinuous Galerkin Method for Convection-Dominated Sobolev Equation

In this paper we shall present, for the convection-dominated Sobolev equations, the fully-discrete numerical scheme based on the local discontinuous Galerkin (LDG) finite element method and the third-order explicitly total variation diminishing Runge-Kutta (TVDRK3) time marching. A priori error estimate is obtained for any piecewise polynomials of degree at most k≥1, under the general spatial-temporal restriction. The bounded constant in error estimate is independent of the reciprocal of the diffusion and dispersion coefficients, after removing the effect of smoothness of the exact solution. Finally some numerical results are given to verify the presented conclusion.