Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations
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- 作者：Waixiang Cao ; Hailiang Liu and Zhimin Zhang
- 刊名：Numerical Methods for Partial Differential Equations
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：33
- 期：1
- 页码：290-317
- 全文大小：200K
- ISSN：1098-2426
文摘
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 -th order superconvergence rate of the DDG approximation at nodes and Lobatto points, respectively, and a -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.