报告题目：Sparse Grid Discontinuous Galerkin Methods for High-Dimensional Elliptic Equations

报告人：Yingda Cheng，Michigan State University

时  间：2015年8月3日    下午4:00―5:00

地  点：东区管理科研楼  数学科学学院1208室

内容提要：

In this talk, we develop an interior penalty method on sparse grid for computations of high-dimensional elliptic equations. 

Using a hierarchical basis representation, we construct a sparse finite element approximation space, reducing the degree 

of freedom from the standard {$O(h^{-d})$ to $O(h^{-1}|/log_2 h|^{d-1})$} for $d$-dimensional problems, where $h$ is the 

uniform mesh size in each dimension. Compared to the traditional full grid approaches, the accuracy of the numerical 

approximation of this method is only slightly deteriorated by a factor of $|/log_2 h|^{d-1}$ in the energy norm. Error estimates 

are provided and confirmed by numerical tests in multi-dimensions

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