Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems - Archive ouverte HAL Access content directly
Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2015

Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Abstract

A reduced basis nite element heterogeneous multiscale method (RB-FE-HMM) for a class of nonlinear homogenization elliptic problems of nonmonotone type is introduced. In this approach, the solutions of the micro problems needed to estimate the macroscopic data of the homogenized problem are selected by a Greedy algorithm and computed in an o ine stage. It is shown that the use of reduced basis (RB) for nonlinear numerical homogenization reduces considerably the computational cost of the nite element heterogeneous multiscale method (FE-HMM). As the precomputed microscopic functions depend nonlinearly on the macroscopic solution, we introduce a new a posteriori error estimator for the Greedy algorithm that guarantees the convergence of the online Newton method. A priori error estimates and uniqueness of the numerical solution are also established. Numerical experiments illustrate the e ciency of the proposed method.
Fichier principal
Vignette du fichier
rbfehmm_nonlin.pdf (2.05 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00811490 , version 1 (10-04-2013)
hal-00811490 , version 2 (30-04-2013)

Identifiers

Cite

Assyr Abdulle, Yun Bai, Gilles Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Discrete and Continuous Dynamical Systems - Series S, 2015, 8 (1), pp.91-118. ⟨10.3934/dcdss.2015.8.91⟩. ⟨hal-00811490v2⟩
332 View
180 Download

Altmetric

Share

Gmail Facebook X LinkedIn More