@Article{IJNAM-14-762,
author = {Zhijian Rong, Jie Shen and Haijun Yu},
title = {A Nodal Sparse Grid Spectral Element Method for Multi-Dimensional Elliptic Partial Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {4-5},
pages = {762--783},
abstract = {<p style="text-align: justify;">We develop a sparse grid spectral element method using nodal bases on Chebyshev-Gauss-Lobatto points for multi-dimensional elliptic equations. Since the quadratures based on
sparse grid points do not have the accuracy of a usual Gauss quadrature, we construct the mass
and stiffness matrices using a pseudo-spectral approach, which is exact for problems with constant
coefficients and uniformly structured grids. Compared with the regular spectral element method,
the proposed method has the flexibility of using a much less degree of freedom. In particular,
we can use less points on edges to form a much smaller Schur-complement system with better
conditioning. Preliminary error estimates and some numerical results are also presented.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10060.html}
}