A Nodal Sparse Grid Spectral Element Method for Multi-Dimensional Elliptic Partial Differential Equations
Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 762–783
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10060
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 762–783
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Sparse grid spectral element method high-dimensional problem adaptive method.