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Advances in Mathematical Physics
Volume 2016, Article ID 4691759, 13 pages
Research Article

A Type of Multigrid Method Based on the Fixed-Shift Inverse Iteration for the Steklov Eigenvalue Problem

School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China

Received 17 March 2016; Revised 9 May 2016; Accepted 10 May 2016

Academic Editor: Luigi C. Berselli

Copyright © 2016 Feiyan Li and Hai Bi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the Steklov eigenvalue problem, we establish a type of multigrid discretizations based on the fixed-shift inverse iteration and study in depth its a priori/a posteriori error estimates. In addition, we also propose an adaptive algorithm on the basis of the a posteriori error estimates. Finally, we present some numerical examples to validate the efficiency of our method.