Superconvergence of Discontinuous Finite Element Solutions for Transient Convection-diffusion Problems

We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivative of Radau polynomial of degree p+ 1. Using these results, we construct several asymptotically exact a posteriori nite element error estimates. Computational results reveal that the error estimates are asymptotically exact.