Superconvergence of local discontinuous Galerkin methods for one-dimensional convectiondiffusion equations
In this paper, we study the convergence behavior of the local discontinuous Galerkin (LDG) methods when applied to one-dimensional time dependent convectiondiffusion equations. We show that the LDG solution will be superconvergent towards a particular projection of the exact solution, if this projection is carefully chosen based on the convection and diffusion fluxes. The order is observed to be at least k+2 k + 2 when piecewise Pk P k polynomials are used. Moreover, the numerical traces for the solution are also superconvergent, sometimes, of higher-order. This is a continuation of our previous work [Cheng Y, Shu C-W. Superconvergence and time evolution of discontinuous Galerkin finite element solutions. J Comput Phys 2008;227:961227], in which superconvergence of DG schemes for convection equations is discussed.
superconvergence local discontinuous galerkin method convectiondiffusion equations projection error estimates