报告题目：Numerical approximation of partial differential equations involving fractional differential operators

报告人：Wenyu Lei (雷闻宇), Texas A&M University

报告时间：12月19日  3:00-4:00

地点：1518

摘要： In this talk, we consider the numerical approximation of partial differential equations (PDEs) involving fractional differential operators. In higher dimensional spaces, fractional differential operators are defined using eigenfunction expansions in the bounded domain case or the Fourier transform when the domain is the whole space. Classical PDE theories still apply to these types of problems since the bilinear forms are bounded and coercive on the appropriate intermediate space between L^2 and H^1_0. Using the finite element method and a so-called sinc quadrature scheme, we focus on the following two topics: approximating parabolic equations involving fractional powers of elliptic operators which come from eigenfunction expansions and the approximation of a variational problem on bounded domain involving fractional operators defined in terms of the Fourier transform.