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A multilevel correction method for Stokes eigenvalue problems and its applications
Author(s) -
Lin Qun,
Luo Fusheng,
Xie Hehu
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2866
Subject(s) - eigenvalues and eigenvectors , finite element method , multigrid method , mathematics , scheme (mathematics) , space (punctuation) , mixed finite element method , stokes problem , mathematical analysis , mathematical optimization , partial differential equation , computer science , physics , quantum mechanics , thermodynamics , operating system
In this paper, a new multilevel correction scheme is proposed to solve Stokes eigenvalue problems by the finite element method. This new scheme contains a series of correction steps, and the accuracy of eigenpair approximation can be improved after each step. In each correction step, we only need to solve a Stokes problem on the corresponding fine finite element space and a Stokes eigenvalue problem on the coarsest finite element space. This correction scheme can improve the efficiency of solving Stokes eigenvalue problems by the finite element method. As applications of this multilevel correction method, a multigrid method and an adaptive finite element technique are introduced for Stokes eigenvalue problems. Some numerical results are given to validate our schemes. Copyright © 2013 John Wiley & Sons, Ltd.