Giani, Stefano and Grubišic, Luka and Hakula, Harri and Ovall, Jeffrey S. (2021) 'A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques.', Journal of scientific computing., 88 (3). p. 55.
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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1007/s10915-021-01572-2|
|Publisher statement:||This is a post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final authenticated version is available online at: https://doi.org/10.1007/s10915-021-01572-2|
|Date accepted:||20 June 2021|
|Date deposited:||21 June 2021|
|Date of first online publication:||20 July 2021|
|Date first made open access:||27 January 2023|
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