报告题目： New space-time spectral and structured spectral element methods for high order probelms（高阶问题的新时空谱和谱元方法）
报告时间：2018年11月29日16:00-17:00
报告地点：理学院二楼会议室
报告人：张超
报告摘要：We propose new space-time spectral and structured spectral element methods for high order problems. By matrix decomposition, we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients. Based on new basis functions in space and a dual-Petrov-Galerkin formulation in time, we propose a new space-time spectral method for a time-dependent problem, and proved their spectral accuracy both in space and time. Numerical results demonstrate their high efficiency and coincide well with theoretical analysis. Further, to ultimately promote the numerical performance and efficiency, we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high-order problems. Besides, to increase the flexibility, aC1-conforming rectangular spectral method in analogy to Argyris or Bell triangular elements are proposed for fourth-order equations, which serves as a preparative work towards conforming quadrilateral spectral elements for high-order equations.