Numerical homogenization for nonlinear strongly monotone problems. (25th February 2021)

• Record Type: Journal Article
• Authors: Verfürth, Barbara
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 2(2022)
• Page Start: 1313
• Page End: 1338
• Publication Date: 2021-02-25
• Subjects: multiscale method -- numerical homogenization -- nonlinear monotone problem -- a priori error estimates; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab004
• Languages: English
• ISSNs: 0272-4979

Abstract

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