Since the first application to three-dimensional turbulence simulation using the Fourier-spectral method at early 1970's, there is a phenomenal growth in the analysis and applications of the spectral and spectral-element methods. The main characteristic of spectral and spectral element methods is the use of high-order polynomials as basis functions, as compared to low-order piecewise polynomials in a finite element method. The main advantage of the spectral methods lies on the fact that the convergence of numerical solutions is exponential if the exact solution is smooth. While the classical spectral methods are limited to simple geometries, the development of the spectral element method allows to take advantages of the geometric flexibility of finite elements and the high accuracy of spectral methods. Undoubtedly the spectral and spectral element methods have become a major computational tool, especially when highly accurate solutions are needed.

The first workshop in the series was held during June 14-16,2007 at Xiamen University.

This third workshop is sponsored by E-institute and Scientific Computing Key Laboratory of Shanghai Universities.  

• Yujian Jiao, Shanghai Normal University, China
• Jie Shen, Purdue University, USA
• Zhongqing Wang, Shanghai Normal University, China
• Chuanju Xu, Xiamen University, China