An H-m -conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues

作者：Han, JiaYu; Yang, YiDu^*

来源：Science China Mathematics, 2017, 60(8): 1529-1542.

DOI：10.1007/s11425-015-0847-y

• spectral element method
• multi-dimensional domain
• interpolation error estimates
• transmission eigenvalues

We develop an H-m-conforming (m >= 1) spectral element method on multi-dimensional domain associated with the partition into multi -dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that are made up of the generalized Jacobi polynomials (CJPs) and the nodal basis functions. So the basis functions on multi -dimensional rectangles consist of the tensorial product of the basis functions on the interval [-1, 1]. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally, we apply the H-2-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.

• 出版日期2017-8
• 单位贵州师范大学