Abstract: Maximum principle preserving is an important property of the entropy solution to the scalar hyperbolic conservation laws. One would like to imitate the property on the numerical level. On the other hand, preserving the maximum principle also provides stability to the numerical schemes for solving the conservation law problem. The challenge exists when solving the conservation law problems with high order schemes in a consistent and conservative framework. In this talk, we will discuss how this problem is addressed by introducing maximum principle flux limiters and address the accuracy and CFL constraint concern. Generalization of the technique to convection-diffusion problem and positivity preserving high order methods for compressible Euler equations will also be discussed.

 

About the Speaker: Zheng-Fu Xu received his B.Sc. and M. Sc in Mathematics from the Department of Mathematics at Peking University. Then he went on to the division of applied mathematics at Brown University for his graduate studies.  He got an M.Sc (minor in computer science) and PhD of applied mathematics from Brown University. After his graduation, he worked as the S Chowla research assistant professor in the department of mathematics at Penn State University. Before he moved to the Michigan Technological University, he worked as research assistant professor in the department of mathematics at Michigan State University. He is now an Associate Professor at the Department of Mathematics in Michigan Technological University, USA. His research focuses on high order numerical methods for solving partial differential equation. His interest of research also includes inverse problems, mathematical imaging, and nonlinear optics.