Efendiev, Y.; Galvis, J.; Presho, M.; Zhou, J. A multiscale enrichment procedure for nonlinear monotone operators. (English) Zbl 1312.65207 ESAIM, Math. Model. Numer. Anal. 48, No. 2, 475-491 (2014). Multiscale finite element methods and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. The nonlinearity of the operator presents additional difficulties that must be considered. The proposed method requires the solutions of (small dimension and local) nonlinear eigenvalue problems in order to systematically enrich the coarse solution space. In order to confirm the methods, a number of numerical examples is presented. Reviewer: Ariadna Lucia Pletea (Iaşi) Cited in 4 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J60 Nonlinear elliptic equations 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs Keywords:generalized multiscale finite element method; domain decomposition; nonlinear elliptic problems; nonlinear eigenvalue problem; numerical example PDFBibTeX XMLCite \textit{Y. Efendiev} et al., ESAIM, Math. Model. Numer. Anal. 48, No. 2, 475--491 (2014; Zbl 1312.65207) Full Text: DOI