# Meeting Details

Title: H\"older estimates for Green's functions on convex polyhedral domains and their applications to finite element methods. CCMA PDEs and Numerical Methods Seminar Series Dmitriy Leykekhman, UCONN In this talk I will explain new sharp H\"older type Green's function estimates for the second order elliptic operator on convex a polyhedral domain. As an applications of these estimates to finite element methods, I will derive the best approximation property of the error in $W^1_{\infty}$ norm. In contrast to previously known results, $W_p^{2}$ regularity for $p>3$, which does not hold for general convex polyhedral domains, is not required. Furthermore, the new Green's function estimates allow us to obtain localized error estimates at a point.