Abstract In this study, for the first time, we discuss the posteriori error estimates and adaptive algorithm for the non-self-adjoint Steklov eigenvalue problem in inverse scattering. The differential operator corresponding to this problem is non-self-adjoint and the associated weak formulation is not H 1-elliptic. Based on the study of Armentano et al. [Appl. Numer. Math. 58 (2008), 593–601], we first introduce error indicators for primal eigenfunction, dual eigenfunction, and eigenvalue. Second, we use Gårding’s inequality and duality technique to give the upper and lower bounds for energy norm of error of finite element eigenfunction, which shows that our indicators are reliable and efficient. Finally, we present numerical results to validate our theoretical analysis.

中文翻译：

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逆散射中Steklov特征值问题的自适应有限元方法

摘要 本研究首次讨论了逆散射中非自伴随Steklov特征值问题的后验误差估计和自适应算法。对应于这个问题的微分算子是非自伴随的，相关的弱公式不是 H 1-椭圆。基于 Armentano 等人的研究。[申请。数字。数学。58 (2008), 593–601]，我们首先介绍了原始特征函数、对偶特征函数和特征值的误差指标。其次，我们使用 Gårding 不等式和对偶技术给出了有限元特征函数误差能量范数的上下界，这表明我们的指标是可靠和有效的。最后，我们提供数值结果来验证我们的理论分析。