Postprocessing and higher order convergence for the mixed finite element approximations of the eigenvalue problem

Authors:
Hongtao Chen;Shanghui Jia;Hehu Xie
Affiliations:
LSEC, ICMSEC, Academy of Mathematics and Systems Science and Graduate University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, China;School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081, China;LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Institute for Analysis and Computational Mathematics, Otto-von-Guericke-University ...
Venue:
Applied Numerical Mathematics
Year:
2011

Citing 5
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Abstract

In this paper, we propose a method to improve the convergence rate of the lowest order Raviart-Thomas mixed finite element approximations for the second order elliptic eigenvalue problem. Here, we prove a supercloseness result for the eigenfunction approximations and use a type of finite element postprocessing operator to construct an auxiliary source problem. Then solving the auxiliary additional source problem on an augmented mixed finite element space constructed by refining the mesh or by using the same mesh but increasing the order of corresponding mixed finite element space, we can increase the convergence order of the eigenpair approximation. This postprocessing method costs less computation than solving the eigenvalue problem on the finer mesh directly. Some numerical results are used to confirm the theoretical analysis.