报告题目：Fully Nonlinear Partial Differential Equations and Their Numerical Solution

报告人：凤小兵(Feng Xiaobing),美国田纳西大学(Knoxville)数学系教授

时间：2012年11月1日(星期四) 16:00-17:00

地点：理科楼数学系A304

摘要：In the past thirty years tremendous progresses have been made on the development of the viscosity solution theory for fully nonlinear (2nd) order PDEs. However, in contrast with the success of the PDE theory, there has been essentially no progress on how to reliably compute these viscosity solutions until very recently. This lack of progress is due to the facts that (1) the notion of viscosity solutionsis non-variational and non-constructive, hence, it is extremely difficultto mimic at the discrete level; (2) viscosity solutions often are only conditionally unique, which is also very difficult to deal with at the discrete level. In this talk, I shall first review some recent developments (and attempts) in numerical methods for fully nonlinear 2nd order PDEs such as the Monge-Ampere type equations and Hamilton-Jacobi-Bellman equations. I shall then present some latest advances on developing finite difference and discontinuousGalerkin (DG) methods for those PDEs. The focus of this talk is to present a newly developed framework for constructing finite difference and DG methods which can reliably approximate viscosity solutions of those fully nonlinear PDEs.The connection between this new framework with the well-knownfinite difference and DG framework for 1st order fullynonlinear Hamilton-Jacobi equations will also be discussed.

联系人：简怀玉