The Influence Of Mesh Structure For Local Discontinuous Galerkin Method

The local discontinuous Galerkin (LDG) method is an efficient method for the convection-diffusion equation, but the specific impact of mesh structure to the numerical solution can not be ignored. In this paper, we use piecewise quadratic polynomials as finite element space with 3rd order explicit total variation diminishing Runge-Kutta time-marching. Through a large number of numerical experiments, we make meticulous numerical observation of the results on different grids. Owing to the different match-ing of the flowing direction, the numerical results perform distinctly in four issues including the smoothness of the contours in the transition layer, the similarity of the contours as the flowing direction, the compactness of contours and the preserving of the shape of trasition layer.