A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

作者：Rong, Zhijian; Shen, Jie; Yu, Haijun^*

来源：International Journal of Numerical Analysis and Modeling, 2017, 14(4-5): 762-783.

• Sparse grid
• spectral element method
• high-dimensional problem
• adaptive method

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.

• 出版日期2017
• 单位中国科学院数学与系统科学研究院; 中国科学院大学; 厦门大学