| Abstract: | 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 the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics. |
