Title: 
Superconvergence of spectral collocation/p-version methods 
in 1-D

Speaker: Zhimin Zhang, Wayne State University

Abstract: 
Superconvergence phenomenon of the Legendre spectral 
collocation method and the p-version finite element
method is discussed under the one dimensional setting. 
For a class of functions that satisfy a regularity condition 
on a bounded domain, it is demonstrated, both theoretically 
and numerically, that the optimal convergent rate is 
super-geometric. Furthermore, at proper Gaussian points or 
Lobatto points, the rate of convergence may gain one or two 
orders of the polynomial degree.