January 25 - 27, 2007

On estimators for eigenvalue/eigenvector approximations

Jeff Ovall (MPI Leipzig)

Using the 2D Dirichlet Laplacian on a (potentially) non-convex domain as a model problem, we consider the reliable assessment of finite element approximations of repeated eigenvalues and their associated invariant subspaces. After motivating our way of measuring the quality of the approximation - which we call approximation defects, much of the talk will focus on establishing that our computable estimates of the approximation defects are reliable, and in many practical cases asymptotically exact (sometimes provably so).

This is joint work with L. Grubisic.

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