An \(H^m\)-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues (Q1703801)

Using the Jacobi polynomials the authors build up in the first instance, on the standard one-dimensional interval, the nodal as well as the modal basis functions. Then by an affine mapping and tensorial product they obtain the basis functions on the multi-dimensional rectangular element. Thus they construct the spectral element interpolation operator and prove the associated interpolation error estimates. A Helmholtz transmission eigenvalue problem in a classical weak formulation is solved on some polyhedral domains. The numerical results are reported in five tables and two figures.