A Brief Survey on High Order Numerical Methods for Convection Dominated Problems

摘要：

　　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 presentation 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.Examples of recent development and applications of these methods will also be discussed.

关键词： Convection dominated PDE high order accurate numerical methods weighted essentially non-oscillatory discontinuous Galerkin methods spectral methods

作者: Chi-Wang Shu

作者单位: DIVISION OF APPLIED MATHEMATICS, BROWN UNIVERSITY PROVIDENCE, RI 02912, USA

会议类型: 国际会议

会议名称: The 6th International Congress of Chinese Mathematicians (第6届世界华人数学家大会)

会议地点: 台北

会议语种:英文

页码: 119-133

在线出版日期: 2013-07-14（万方平台首次上网日期，不代表论文的发表时间）