报告人：曹外香（中山大学）

报告题目：Superconvergence of Discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations

报告摘要：In this talk, we present superconvergence properties of the discontinuous Galerkin method using upwind-biased numerical fluxes for one-dimensional linear hyperbolic equations. A (2k + 1)-th order superconvergence rate of the DG approximation at the numerical fluxes and for the cell average is obtained under quasi-uniform meshes and some suitable initial discretization, when piecewise polynomials of degree k are used. Furthermore, surprisingly, we find that the derivative and function value approximation of the DG solution are superconvergent at a class of special points, with an order k + 1 and k+2, respectively. These superconvergent points can be regarded as the generalized Radau points. All theoretical findings are confirmed by numerical experiments.    

报告人简介：曹外香，中山大学数据科学与计算机学院 特聘研究员。 主要从事间断有限元方法、有限体积方法超收敛等方面的研究工作， 在SINUM， Math. Comp 等计算数学顶级杂志发表多篇重要学术论文。

报告时间：2017年7月3日（星期一）上午10:00-11:30

报告地点：科技楼南楼602