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 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. [ABSTRACT FROM AUTHOR]