The multilevel mixed finite element discretizations based on local defect-correction for the Stokes eigenvalue problem

Abstract Based on the work of Xu and Zhou (2000), this paper combines mixed finite element method and the local defect-correction technique to establish new local and parallel multilevel discretization schemes for the Stokes eigenvalue problem. Theoretical analysis and numerical experiments show that the computational approach proposed in this paper is simple and easy to carry out in parallel, and can be used to solve singular Stokes eigenvalue problem efficiently. This paper also discusses local error estimates of mixed finite element approximations; it is a new feature here that the estimates apply to the local domains containing corner points.

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