An Immersed Finite Element Approach Based on Dimensional Reduction for Elliptic Interface Eigenvalue Problems with Radial Stratified Media

Abstract In this paper, a novel and efficient immersed finite element approach based on dimensionalreduction is proposed and studied for elliptic interface eigenvalue problems with radialstratified media. Firstly, the original problem is decomposed into a series of decoupled one-dimensional second-order interface eigenvalue problems by introducing appropriate coordinate transformations. Subsequently, a class of weighted Sobolev spaces and their approximation spaces are defined in accordance with the boundary conditions and interface jump conditions, based on which, the variational form and its discrete scheme are established for each one-dimensional second-order interface eigenvalue problem, and the error estimates for the approximation eigenvalues and eigenfunctions are theoretically proved. Finally, some numerical experiments are presented to demonstrate the stability and convergence of the algorithm.