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 \(\mathbb {R}^{d}~(d=2,3)\). An adaptive algorithm based on the a posteriori error estimators is designed. Numerical results are provided to illustrate the efficiency of our adaptive algorithm.

中文翻译：

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不同弹性张量和不同质量密度弹性传递特征值问题的自适应有限元法

由逆散射理论产生的弹性传输特征值问题在弹性介质的定性重建方法中起着至关重要的作用。本文提出并分析了有限元法的后验误差估计器，用于求解\(\mathbb {R}^{d}~(d=2,3)中不同弹性张量和不同质量密度的弹性传递特征值问题\)。设计了一种基于后验误差估计器的自适应算法。提供数值结果来说明我们的自适应算法的效率。