Reliable a-posteriori error estimators for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems

Details Reliable a-posteriori error estimators for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems Reliable a-posteriori error estimators for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems

2011-12-02

arxiv.org/abs/1112.0436v1

Mathematics

Numerical Analysis

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Scientific paper

We present reliable a-posteriori error estimates for $hp$-adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on $h$ adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the $hp$-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.

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