非自伴elliptic differential operators大缺陷特征值的基准计算
Benchmark computation of eigenvalues with large defect for non-selfadjoint elliptic differential operators
摘要：
本文给出了一类具有大缺陷和大上升的非自伴椭圆型本征值问题的基准问题。我们描述了一个不连续系数和混合边界条件的基准问题的推导。通过数值实验研究了Galerkin有限元法的收敛性与离散参数、问题的正则性和特征值的上升率的关系。这使我们能够验证这些参数的理论估计从文献的尖锐性。我们提供了数值证据的上升的大小，并表明，重要的是要考虑的平均值的特征值近似。
英文摘要：
In this paper we present benchmark problems for non-selfadjoint elliptic eigenvalue problems with large defect and ascent. We describe the derivation of the benchmark problem with a discontinuous coefficient and mixed boundary conditions. Numerical experiments are performed to investigate the convergence of a Galerkin finite element method with respect to the discretization parameters, the regularity of the problem, and the ascent of the eigenvalue. This allows us to verify the sharpness of the theoretical estimates from the literature with respect to these parameters. We provide numerical evidence about the size of the ascent and show that it is important to consider the mean value for the eigenvalue approximation.
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