CAM seminar——Numerical approximation for nonlocal problems
报告人：Wenbo Li (The University of Tennessee, Knoxville)
We consider problems involving nonlocality in time or space. First, we consider a so-called fractional gradient flow: an evolution equation aimed at the minimization of a convex and lower semicontinuous energy, but where the evolution has memory effects and is described by the so-called Caputo derivative. We introduce the notion of energy solutions, for which we provide existence, uniqueness, and certain regularizing effects. We derive an a posteriori error estimate and show its reliability. Second, we discuss two nonlocal and nonlinear variational problems: the nonlocal minimal graph problem and the fractional p-Laplacian. We discuss regularity of solutions to these problems, propose finite element methods to numerically solve them, and analyze their convergence properties.
Wenbo Li is a postdoc at the Department of Mathematics at the University of Tennessee, Knoxville. He received his PhD degree at the University of Maryland under the supervision of Ricardo H. Nochetto. Wenbo's research focuses on the numerical analysis of partial differential equations and related questions. He has mainly worked on two classes of problems: nonlocal problems and strongly nonlinear elliptic PDEs.