Penn State University

Interdisciplinary Seminar on PDEs and their Applications

Meeting on (joint with the CCAM Seminar on PDE & Numerical Methods)

Monday, April 14th, 2008, 3:30PM

MB 315, University Park

Speaker:

Dmitriy Leykekhman

Department of Mathematics
University of Connecticut

Title:

Hölder estimates for Green's functions on convex polyhedral domains
and their applications to finite element methods

Abstract:

In this talk I will explain new sharp Hölder 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^2_p 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.