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Scientific article
English

Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

Published inMultiscale modeling & simulation, vol. 13, no. 3, p. 916-952
Publication date2015
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
Research group
Funding
  • Swiss National Science Foundation - 200020144313/1.
Citation (ISO format)
ABDULLE, Assyr, HUBER, Martin, VILMART, Gilles. Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. In: Multiscale modeling & simulation, 2015, vol. 13, n° 3, p. 916–952. doi: 10.1137/140975504
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Article (Submitted version)
accessLevelPublic
Identifiers
ISSN of the journal1540-3459
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Technical informations

Creation11/12/2014 3:54:00 PM
First validation11/12/2014 3:54:00 PM
Update time03/15/2023 12:02:20 AM
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