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Title

Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems
Authors
Abdulle, Assyr
Huber, Martin
Vilmart, Gilles
Published in Multiscale Modeling and Simulation. 2015, vol. 13, no. 3, p. 916–952
Abstract We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the microscopic scales. It can be interpreted as a linearized version of a standard nonlinear homogenization method. We prove the stability of the method and derive optimal a priori error estimates which are fully discrete in time and space. Numerical experiments confirm the error bounds and illustrate the efficiency of the method for various nonlinear problems.
Keywords Monotone parabolic multiscale problem — Linearized scheme — Numerical homogenization method — Fully discrete a priori error estimates
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Article (Preprint) (4.7 MB) - public document Free access
Other version: http://dx.doi.org/10.1137/140975504
Structures
Faculté des sciences / Section de mathématiques
Research group Analyse numérique
Project FNS: 200020144313/1.
Citation
(ISO format) 		ABDULLE, Assyr, HUBER, Martin, VILMART, Gilles. Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. In: Multiscale Modeling and Simulation, 2015, vol. 13, n° 3, p. 916–952. https://archive-ouverte.unige.ch/unige:79120

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Deposited on : 2016-01-12

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