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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1529-1542
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-015-0847-y

摘要

We develop an Hm-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 (GJPs) 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 H2-conforming spectral element method to thc Hclmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.