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On the approximation of the spectrum of the Stokes operator. (English) Zbl 0683.65095
The Stokes problem is considered in a bounded domain. It is proved that there exists an infinite sequence of eigenvalues and a corresponding sequence of eigenfunctions of the Stokes operator. Error estimates are derived for the approximate calculation of the eigenvalues of the Stokes operator. These estimates are valid for the regularized version of mixed methods which are used for the approximate solution of the Stokes problem.
Reviewer: Z.Dżygadło
MSC:
65N25Numerical methods for eigenvalue problems (BVP of PDE)
65N15Error bounds (BVP of PDE)
76D07Stokes and related (Oseen, etc.) flows
35P15Estimation of eigenvalues and upper and lower bounds for PD operators