Cao, Liqun; Zhang, Lei; Allegretto, Walter; Lin, Yanping Multiscale asymptotic method for Steklov eigenvalue equations in composite media. (English) Zbl 1267.65172 SIAM J. Numer. Anal. 51, No. 1, 273-296 (2013). 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. Reviewer: Wilhelm Heinrichs (Essen) Cited in 19 Documents 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 Keywords:multiscale asymptotic expansion; boundary layer solution; numerical examples; convergence; eigenfunctions PDFBibTeX XMLCite \textit{L. Cao} et al., SIAM J. Numer. Anal. 51, No. 1, 273--296 (2013; Zbl 1267.65172) Full Text: DOI Link