Local and Parallel Finite Element Schemes for the Elastic Transmission Eigenvalue Problem

Abstract

Local and parallel finite element computations for the elastic transmission eigenvalue problem are studied in this paper. After deriving the local a priori error estimates for finite element approximations of the problem, we establish local and parallel finite element schemes, which include classical conforming finite elements and spectral elements for the problem with local low smooth eigenfunctions. The errors of the method are analysed and numerical examples show the efficiency of the schemes.