Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems
نویسندگان
چکیده
منابع مشابه
Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems
We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapidly at a microscopic scale. The multiscale method approximates the homogenized solution at computational cost independent of the small scale b...
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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 m...
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Article history: Received 27 August 2009 Received in revised form 29 April 2010 Accepted 8 June 2010 Available online 18 June 2010
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An analysis of the finite element heterogeneous multiscale method for a class of quasilinear elliptic homogenization problems of nonmonotone type is proposed. We obtain optimal convergence results for dimension d ≤ 3. Our results, which also take into account the microscale discretization, are valid for both simplicial and quadrilateral finite elements. Optimal a-priori error estimates are obta...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2016
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2016003