A multilevel correction method for Stokes eigenvalue problems and its applications. (3rd June 2013)

• Record Type: Journal Article
• Authors: Lin, Qun; Luo, Fusheng; Xie, Hehu
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 18(2015:Dec. 15)
• Page Start: 4540
• Page End: 4552
• Publication Date: 2013-06-03
• Subjects: Stokes eigenvalue problem -- finite element method -- multilevel correction -- multigrid -- adaptive technique; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2866
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.