Seminars on Numerical Algorithms, Analyses, and Applications：Analysis of a finite element method for second order uniformly elliptic PDEs in non-divergence form

报告人：邱蔚峰（香港城市大学）

时  间：2026年5月6日10:30

地  点：海韵园行政楼C503

内容摘要:

We propose one finite element method for both second order linear uniformly elliptic PDE in non-divergence form and the uniformly elliptic Hamilton-Jacobi-Bellman (HJB) equation. For both linear elliptic PDE in non-divergence form and the HJB equation,  we prove the well-posedness of strong solution in W^{2,p} and optimal convergence in discrete W^{2,p}-norm of the finite element approximation to the strong solution for 1<p<= 2 on convex polyhedra in $R}^d (d=2,3). If the domain is a two dimensional non-convex polygon, p is valid in a more restricted region. Furthermore, we relax the assumptions on the continuity of coefficients of the HJB equation, which have been widely used in literature.

个人简介：

Prof. Weifeng Qiu received his BSc from Shanghai Normal University in 2000, Master from University of Alabama in Huntsville in 2006, and PhD from the University of Texas at Austin in 2010. His PhD advisor is Professor Leszek Demkowicz. Before joining City University in 2012, he worked as a Postdoctoral Fellow at IMA (Institute for Mathematics and Its Applications), University of Minnesota. His postdoctoral mentor is Professor Bernardo Cockburn. His major research interests include scientific computing and numerical analysis for PDE. He has published his research in established journals, including SIAM Journal on Numerical Analysis, Mathematics of Computation, and Numerische Mathematik.

联系人：陈黄鑫