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A type of multilevel method for the Steklov eigenvalue problem. (English) Zbl 1312.65178
A multilevel method for computing finite element approximations to the Steklov eigenvalue problem is presented.
An eigenpair approximation on the coarsest level space is improved by applying a sequence of correction steps performed in increasingly refined nested level spaces. Each correction step involves the finite element approximation of a boundary value problem on the corresponding refined level as well as the solution of a low-dimensional eigenvalue problem on a 1D augmented version of the coarsest level space.
It is shown that this improved eigenpair approximation arrives at the same optimal error estimates as the direct approximation of the Steklov eigenvalue problem on the finest level.
Moreover, the amount of computational work is proportional to the dimension of the finest finite element space.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
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