TY - JOUR
T1 - A Nodal Sparse Grid Spectral Element Method for Multi-Dimensional Elliptic Partial Differential Equations
AU - Zhijian Rong, Jie Shen & Haijun Yu
JO - International Journal of Numerical Analysis and Modeling
VL - 4-5
SP - 762
EP - 783
PY - 2017
DA - 2017/08
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10060.html
KW - Sparse grid, spectral element method, high-dimensional problem, adaptive method.
AB - <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>