Affiliation:
1. Institut für Angewandte und Numerische Mathematik, Karlsruher Institut für Technologie, Englerstr. 2, D-76131 Karlsruhe, Germany
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.
Funder
Deutsche Forschungsgemeinschaft
Federal Ministry of Education and Research
Baden-Württemberg Ministry of Science
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
Cited by
2 articles.
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