[Lecture] CAM Seminar—Recent Developments in Numerical Methods for Fully Nonlinear PDEs
Title: CAM Seminar—Recent Developments in Numerical Methods for Fully Nonlinear PDEs
Time: January 3, 2020, 15:00-16:00
Venue: Room 1560, Sciences Building No. 1
Speaker: Feng Xiaobing (The University of Tennessee)
Abstract: In this talk, I shall first present a brief overview about recent advances in numerical fully nonlinear PDEs. I shall then discuss in details a newly developed narrow-stencil finite difference framework for approximating viscosity solutions of fully nonlinear second order PDEs (such as Hamilton-Jacobi-Bellman and Monge-Ampere equations). The focus of the talk will be on discussing how to compensate the loss of monotonicity of the schemes (due to the use of narrow stencils) in order to ensure the convergence of the schemes, and to explain some key new concepts such as generalized monotonicity, consistency and numerical moment. The connection between the proposed methods and some well-known finite difference methods for first order Hamilton-Jacobi equations will be explained. Finally I shall briefly explain how to extend these finite difference techniques to a (high order) discontinuous Galerkin setting.
Edited by: Qiu Tianjie
Source: School of Mathematical Sciences