A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem (Communications in Computational Physics, 2021)
The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with otherlow-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple toimplement.
Keywords: Elastic transmission eigenvalue problem; nonconforming finite element method; high accuracy