Korean J. Math. Vol. 26 No. 3 (2018) pp.467-481
DOI: https://doi.org/10.11568/kjm.2018.26.3.467

Postprocessing for the Raviart--Thomas mixed finite element approximation of the eigenvalue problem

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Published: Sep 30, 2018
Keywords:
eigenvalue problem, mixed finite element method, super- convergence, postprocessing, asymptotic exactness.
Mathematics Subject Classification:
65N25, 65N30.

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Kwang-Yeon Kim
Department of Mathematics Kangwon National University Chun-Cheon 24341, Korea

Abstract

In this paper we present a postprocessing scheme for the Raviart--Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the L2 errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.


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Supporting Agencies

This study is supported by 2015 Research Grant from Kangwon National Univer- sity (No. D1000412-01-01).

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