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Numerical homogenization for nonlinear strongly monotone problems

Verfürth, Barbara

Abstract:
In this work we introduce and analyze 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 beyond periodicity and scale separation and without assuming higher regularity of the solution. The effect of different linearization strategies is discussed in theory and practice. Several numerical examples including stationary Richards equation confirm the theory and underline the applicability of the method.

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Volltext §
DOI: 10.5445/IR/1000122588
Veröffentlicht am 14.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 10.08.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000122588
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 25 S.
Serie CRC 1173 Preprint ; 2020/22
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter multiscale method, numerical homogenization, nonlinear monotone problem, a priori error estimates
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