Applied Mathematics Seminar——Superconvergence of Discountinuous Galerkin Methods
报告人：Zhimin Zhang (Wayne State University)
时间：2026-06-12 16:10-17:10
地点：智华楼-四元厅-225
Abstract:
The phenomenon of superconvergence is well understood for the h-version finite element method, and researchers in this established field have accumulated a vast body of literature over the past 60 years. However, there is a lack of relevant studies for other numerical methods such as the p-version finite element method, spectral methods, discontinuous Galerkin methods, and finite volume methods. We believe that the scientific community would also benefit from studying of superconvergence phenomenon in these methods. In the last decade, efforts have been made to expand the scope of superconvergence. In this talk, we present some developments in the study of superconvergence for discontinuous Galerkin methods.
Bio:
Zhimin Zhang received a B.S. degree in mathematics and an M.S. degree in computational mathematics from the University of Science and Technology of China (USTC) in 1982 and 1985, respectively; and a Ph.D. degree in applied mathematics from the University of Maryland at College Park in 1991. He was appointed as an assistant professor in 1991 and promoted to associate professor in 1997 at Texas Tech University. Subsequently, he held positions as associate professor in 1999 and full professor in 2002 at Wayne State University. His research focuses on numerical methods for partial differential equations, encompassing finite element methods, finite volume methods, and spectral methods. He has authored and/or co-authored more than 260 journal articles. He has been on editorial boards of 10 professiaonal journals iscluding ``Mathematics of Computation” (2009--2017), ``Journal of Scientific Computing (2011--2017), ``Numerical Methods for Partial Differential Equations (since 2013). The polynomial preserving recovery (PPR) method he proposed was adopted by the large commercial software COMSOL Multiphysics in 2008 and has been used ever since. He is a recipient of 2011 Outstanding Graduate Mentor Award and 2014 Charles H. Gershenson Distinguished Faculty Fellows Award, and was elected to Academy of Scholars at Wayne State University in 2024.
