Abstract In this paper, we apply discontinuous Galerkin methods to the non-selfadjoint Steklov eigenvalue problem arising in inverse scattering. The variational formulation of the problem is non-selfadjoint and does not satisfy H1-elliptic condition. By using the spectral approximation theory of compact operators, we prove the spectral approximation and optimal convergence order for the eigenvalues. Finally, some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex Steklov eigenvalues.

中文翻译：

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逆散射中非自伴Steklov特征值问题的不连续伽辽金方法

摘要 在本文中，我们将不连续伽辽金方法应用于逆散射中出现的非自伴随Steklov特征值问题。该问题的变分公式是非自伴的，不满足 H1-椭圆条件。利用紧算子的谱逼近理论，证明了特征值的谱逼近和最优收敛阶数。最后，报告了一些数值实验，表明所提出的数值方案对于实数和复数 Steklov 特征值是有效的。