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Multiscale asymptotic method for Steklov eigenvalue equations in composite media. (English) Zbl 1267.65172

Authors’ abstract: We consider the multiscale analysis of a Steklov eigenvalue equation with rapidly oscillating coefficients arising from the modeling of a composite media with a periodic microstructure. There are mainly two new results in the present paper. First, we obtain the convergence rate with \( \varepsilon^{1/2} \) for the multiscale asymptotic expansions of the eigenvalues and the eigenfunctions of the Steklov eigenvalue problem. Second, the boundary layer solution is defined. Numerical simulations are then carried out to validate the above theoretical results.

MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35B50 Maximum principles in context of PDEs
35P15 Estimates of eigenvalues in context of PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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