报告人：邱蔚峰助理教授

        香港城市大学数学系

报告题目：A superconvergent HDG method for the Incompressible Navier-Stokes Equations  on general polyhedral meshes

报告时间：2016年04月12日下午16:00

报告地点：实验楼105

学院联系人:陈黄鑫副教授

报告摘要: We present a superconvergent hybridizable discontinuous Galerkin (HDG) method for the steady-state incompressible Navier-Stokes equations on general polyhedral meshes. For arbitrary conforming polyhedral mesh, we use polynomials of degree k+1, k, k to approximate the velocity, velocity gradient and pressure, respectively. In contrast, we only use polynomials of degree k to approximate the numerical trace of the velocity on the interfaces. Since the numerical trace of the velocity field is the only globally coupled unknown, this scheme allows a very efficient implementation of the method. For the stationary case, and under the usual smallness condition for the source term, we prove that the method is well defined and that the global L2-norm of the error in each of the above-mentioned variables and the discrete H1-norm of the error in the velocity converge with the order of k+1 for k>=0. We also show that for k>=1, the global L2-norm of the error in velocity converges with the order of k+2. From the point of view of degrees of freedom of the globally coupled unknown: numerical trace, this method achieves optimal convergence for all the above-mentioned variables in L2-norm for k>=0, superconvergence for  the velocity in the discrete H1-norm without postprocessing for k>=0, and superconvergence for the velocity in L2-norm without postprocessing for k>=1.  

报告人简介：邱蔚峰，香港城市大学数学系助理教授，2010年于美国 University of Texas at Austin取得博士学位，2010-2012年于美国 IMA (Institute for Mathematics and Its Applications), University of Minnesota做博士后，研究方向为科学计算、数值分析。

欢迎广大师生参加！