Document Type
Pre-Print
Publication Date
11-13-2020
Abstract
We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate invariant subspaces. Numerical experiments demonstrate the practical effectivity of the approach.
Rights
This is the preprint version, under review for publication in Numerische Mathematik, and is also available at https://arxiv.org/abs/2009.06677.
Persistent Identifier
https://archives.pdx.edu/ds/psu/34268
Citation Details
Giani, S., Grubisic, L., Hakula, H., & Ovall, J. (2020). A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques. Preprint version.