Superconvergence phenomenon is well understood for the h-version finite element method and researchers in this old field have accumulated a vast literature during the past 50 years. However, the relevant study for other numerical methods such as the p-version finite element method, spectral methods, discontinuous Galerkin methods, and finite volume methods is lacking. We believe that the scientific community would also benefit from the study of superconvergence phenomenon of those methods. In recent years, efforts have been made to expand the territory of the superconvergence. In this talk, we present some recent development on superconvergence study for discontinuous Galerkin methods.
张智民，美国韦恩州立大学教授，Charles H. Gershenson 杰出学者，“长江学者奖励计划”讲座教授，曾在世界华人数学家大会45分钟报告。研究方向是偏微分方程数值解，包括有限元，有限体积，谱方法等，发表学术论文200余篇；提出的多项式保持重构Polynomial Preserving Recovery（PPR）格式于2008年被国际上广为流行的大型商业软件 COMSOL Multiphysics 采用，并使用至今。担任或曾任“Mathematics of Computation” “Journal of Scientific Computing” 等9个国际计算数学杂志编委。