## High order numerical methods for convection dominated problems

- Sept. 25, 2015
- 3:45 p.m.
- LeConte 412

## Abstract

Convection dominated partial differential equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations; however they are difficult to design because solutions may contain discontinuities and other singularities or sharp gradient regions. In this talk we will survey several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference methods, WENO finite volume methods, discontinuous Galerkin finite element methods, and spectral methods. We will discuss essential ingredients, properties and relative advantages of each method, and comparisons among these methods. Recent development and applications of these methods will also be discussed.

**Brief Bio:**

Chi-Wang Shu obtained his BS degree from the University of Science and Technology of China in 1982 and his PhD degree from the University of California at Los Angeles in 1986. He came to Brown University as an Assistant Professor in 1987, moving up to Associate Professor in 1992 and Full Professor in 1996. He was the Chair of the Division of Applied Mathematics between 1999 and 2005, and is now the Theodore B. Stowell University Professor of Applied Mathematics. His research interest includes high order finite difference, finite element and spectral methods for solving hyperbolic and other convection dominated partial differential equations, with applications to areas such as computational fluid dynamics, semi-conductor device simulations and computational cosmology. He served as the Managing Editor of Mathematics of Computation between 2002 and 2012, is now the the Chief Editor of Journal of Scientific Computing and serves in the editorial boards of several other journals. His honors include the First Feng Kang Prize of Scientific Computing in 1995 and the SIAM/ACM Prize in Computational Science and Engineering in 2007. He is a SIAM Fellow and an AMS Fellow, and an invited speaker at the International Congress of Mathematicians at Seoul in 2014.