Partial differential equations -- Numerical solutions, Eigenvalues -- Estimation, Eigenvectors
As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.
Giani, Stefano; Grubisic, Luka; and Ovall, Jeffrey S., "Benchmark Results for Testing Adaptive Finite Element Eigenvalue Procedures II (Cluster Robust Eigenvector and Eigenvalue Estimates)" (2012). Mathematics and Statistics Faculty Publications and Presentations. 113.