An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities

The elastic transmission eigenvalue problem, arising from the inverse scattering theory, plays a critical role in the qualitative reconstruction methods for elastic media. This paper proposes and analyzes an a posteriori error estimator of the finite element method for solving the elastic transmission eigenvalue problem with different elastic tensors and different mass densities in \(\mathbb {R}^{d}~(d=2,3)\) ${\mathbb{R}}^d(d=2,3)$ . An adaptive algorithm based on the a posteriori error estimators is designed. Numerical results are provided to illustrate the efficiency of our adaptive algorithm.