Numerical homogenization for nonlinear strongly monotone problems

Abstract In this work we introduce and analyse a new multiscale method for strongly nonlinear monotone equations in the spirit of localized orthogonal decomposition. A problem-adapted space is constructed by solving linear local fine-scale problems, which then used generalized finite element method. The linearity problems allows their localization and, moreover, makes very efficient to use. gives optimal priori error estimates up linearization errors. results neither require structural assumptions on coefficient such as periodicity or scale separation nor higher regularity solution. effect different strategies discussed theory practice. Several numerical examples including stationary Richards equation confirm underline applicability