OPTIMAL ERROR ESTIMATES OF THE SEMIDISCRETE CENTRAL DISCONTINUOUS GALERKIN METHODS FOR LINEAR HYPERBOLIC EQUATIONS

We analyze the central discontinuous Galerkin method for time-dependent linear conservation laws. In one dimension, optimal a priori L-2 error estimates of order k + 1 are obtained for the semidiscrete scheme when piecewise polynomials of degree at most k (k >= 0) are used on overlapping uniform meshes. We then extend the analysis to multidimensions on uniform Cartesian meshes when piecewise tensor-product polynomials are used on overlapping meshes. Numerical experiments are given to demonstrate the theoretical results.