论文标题
A后验误差估计和AM的自适应算法，用于传输各向异性介质的特征值
The a posteriori error estimates and an adaptive algorithm of the FEM for transmission eigenvalues for anisotropic media
论文作者
论文摘要
反向散射理论引起的传播特征值问题在定性方法和实际应用中非常重要。在本文中，我们研究了$ω\ subset \ mathbb {r}^d $，（d = 2,3）中各向异性媒体的传输特征值问题。使用T-钙率和光谱近似理论，我们得出了残留类型的后验估计量，并证明了其对本征函数的有效性和可靠性。此外，我们还证明了传输特征值的估计器的可靠性。数值实验表明我们的方法是有效的，可以通过使用$ m $的分段多项式来达到最佳订单$ dof^{ - 2m/d} $。
The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the transmission eigenvalue problem for anisotropic inhomogeneous media in $Ω\subset \mathbb{R}^d$,(d=2,3). Using the T-coercivity and the spectral approximation theory, we derive an a posteriori estimator of residual type and prove its effectiveness and reliability for eigenfunctions. In addition, we also prove the reliability of the estimator for transmission eigenvalues. The numerical experiments indicate our method is efficient and can reach the optimal order $DoF^{-2m/d}$ by using piecewise polynomials of degree $m$ for real eigenvalues.
