Superconvergence of the Direct Discontinuous Galerkin Method for Convection-Diffusion Equations
نویسندگان
چکیده
This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for one-dimensional linear convection-diffusion equations. We prove, under some suitable choice of numerical fluxes and initial discretization, a 2k-th and (k + 2) -th order superconvergence rate of the DDG approximation at nodes and Lobatto points, respectively, and a (k + 1) -th order of the derivative approximation at Gauss points, where k is the polynomial degree. Moreover, we also prove that the DDG solution is superconvergent with an order k + 2 to a particular projection of the exact solution. Numerical experiments are presented to validate the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 000: 000–000, 2016
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