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A multilevel correction type of adaptive finite element method for Steklov eigenvalue problems. (English) Zbl 1313.65298
Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 134-143 (2012).
This paper proposes a multilevel correction type of adaptive finite element method for Steklov eigenvalue problems. In this method, each adaptive step involves solving associated boundary value problems on the adaptive partitions and a small scale eigenvalue problem on the coarsest partition. Since solving eigenvalue problem in the finest partition is not required, the overfull efficiency of solving Steklov eigenvalue problems can be improved to the similar efficiency of the adaptive finite element method for the associated boundary value problems. The efficiency of the proposed method is also investigated by a numerical experiment. The interesting and efficient adaptive finite element method in this paper can also be extended to other eigenvalue problems.
For the entire collection see [Zbl 1277.00031].

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
35P15 Estimates of eigenvalues in context of PDEs
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