Filtering for Galerkin Methods: Introduction, Application, and Challenge


Speaker:     Dr. Xiaozhou Li
Time:          Jul.19.2021 15:00-16:00
Location:    SIST 2-415
Host:            Prof. Qiu Yue

Superconvergence is one of the well-known beneficial properties of the Galerkin method.  Previous investigations into accuracy enhancement for a Galerkin solution demonstrated many ways to extract the superconvergence in the solution, such as the filtering/post-processing technique. For example, if applied to DG solutions, it can raise the convergence rate from order $k+1$ to order $2k+1$ in the $L^2$ norm. In addition to enhancing the accuracy, the filtering also increases the inter-element smoothness of the original solution. In this talk, we focus on introducing this filtering/post-processing technique: what it is, why it is valid, how to design a generic accuracy-enhancing filter, and some possible applications.

李小舟博士,2010年本科毕业于中国科学技术大学数学系,2015年于荷兰代尔夫特理工大学获得博士学位,2015年至2017在瑞士Università della Svizzera Italiana计算科学研究所、心脏病学计算中心任博士后。20179月至今在电子科技大学数学科学学院任副研究员。主要研究方向为微分方程的高阶精度数值方法(DG方法及其超收敛后处理技术等)、高性能计算等。