Speaker: Professor Qiang Du, Colombia University, USA

Time: 2016-01-08,  4:00-5:00pm

Venue: Room 316 of Environment Building, Renmin University 

Title: Nonlocal vector calculus, nonlocal balance laws and asymptotically 
compatible discretizations

Abstract: Nonlocality is ubiquitous in nature. While partial differential equations (PDE) have been used as effective models of many physical processes, nonlocal balanced laws are also attracting more and more attentions as alternatives to model singularities and anomalous behavior. In this talk, we discuss the mathematical structure of some nonlocal models by exploiting a recently developed nonlocal vector calculus that offers an analogy of classical vector calculus for local PDEs. The latter, when physically valid, may be derived as local limits of their nonlocal counterparts. We also present asymptotically compatible discretizations of nonlocal models that are able to provide convergent approximations both in the nonlocal setting and in the local limit. Such discretizations are more robust for problems with varying length scales.