Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
510792 | Computers & Structures | 2009 | 12 Pages |
In this paper, we study the convergence behavior of the local discontinuous Galerkin (LDG) methods when applied to one-dimensional time dependent convection–diffusion 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+2k+2 when piecewise PkPk 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;227:9612–27], in which superconvergence of DG schemes for convection equations is discussed.