题目：Toward the Efficient and Practical Extension of the Post-processing of Discontinuous Galerkin Method

报告人: 李小舟   电子科技大学数学科学学院

  

时间： 2018年8月7日 下午 2:00-3:00 

地点： 管理科研楼 1218

摘要：

In this talk, we discuss the efficient and practical extension for the post-processing technique (also known as Smoothness-Increasing Accuracy-Conversing filtering) of discontinuous Galerkin (DG) methods for time-dependent partial differential equations.  The post-processing technique is applied at the final time of the DG method, can enhance the accuracy and smoothness of the original DG solution (space superconvergence).  However, there are still some difficulties stand in the theory and practical application of the post-processing.  One difficulty of the post-processing is that the space superconvergence after filtering needs to be matched with proper temporary accuracy. If the semi-discretized system (ODE system after spatial discretization) is under-resolved in time, then the accuracy-enhancing property of the post-processing will be concealed.  Another difficulty is the efficient implementation of the convolution operator of the post-processing.  To evaluate the integral involved in the convolution precisely to machine precision， one needs to respect the breaks in continuity in the integrand.  This is not a problem for uniform meshes, however, the integration can be much complicated than this when we consider unstructured grids.  In this talk, we focus the investigation of the extensions of the post-processing which can overcome the two difficulties mentioned before.