Xu-Ying ZHAO

Beijing Computational Science Research Center
Abstract: Nonlocal models such as nonlocal diffusion equations and nonlocal peridynamic models have attracted much attention recently. In this talk, we present an adaptive finite element algorithm for the numerical solution of a class of nonlocal models which correspond to nonlocal diffusion equations with certain non-integrable kernel functions. The convergence of the adaptive finite element algorithm is rigorously derived with the help of several basic ingredients, such as the upper bound of the estimator, the estimator reduction and the orthogonality property. We also consider how the results are affected by the horizon parameter  which characterizes the range of nonlocality. Numerical experiments are performed to verify our theoretical findings.

Location: 606 Conference Room
Date and time: Feb 24, 2012   14:30