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SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 1, pp. 222 - 271
Journal Article
Mathematics of Computation, ISSN 0025-5718, 2019, Volume 88, Issue 316, pp. 637 - 664
We propose a two-scale finite element method for the Monge-Ampere equation with Dirichlet boundary condition in dimension d >= 2 and prove that it converges to... 
Two-scale method | Monge-Ampère equation | Monotone scheme | Regularization | Viscosity solution | Convergence | MATHEMATICS, APPLIED | Monge-Ampere equation | convergence | two-scale method | regularization | CONVEX-FUNCTIONS | viscosity solution | NUMERICAL-SOLUTION | DISCRETIZATION | MONOTONE | OPERATOR | DIRICHLET PROBLEM | monotone scheme
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2018, Volume 41, Issue 3, pp. 1101 - 1106
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2010, Volume 23, Issue 10, pp. 1170 - 1173
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 05/2018, Volume 28, Issue 5, pp. 979 - 1035
The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in... 
Bidomain model | asymptotic analysis | homogenization | two-scale convergence | MATHEMATICS, APPLIED | REACTION-DIFFUSION SYSTEMS | ELECTRIC-FIELD | SETS | EQUATIONS | CURRENTS | CELL
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2017, Volume 15, Issue 4, pp. 1651 - 1671
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of... 
Cell averaging | Multiscale problems | Periodic homogenization | Two-scale convergence | Boundary layers | multiscale problems | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | periodic homogenization | cell averaging | boundary layers | PHYSICS, MATHEMATICAL | two-scale convergence
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 02/2011, Volume 85, Issue 7, pp. 847 - 873
Journal Article
ESAIM: Proceedings, ISSN 1270-900X, 12/2012, Volume 38, pp. 1 - 35
Those notes are the lecture notes of lectures given at Cemracs 2011 Summer School. I present here the classical results of Two-Scale Convergence Theory and an... 
Homogenization | Partial differential equations | Lectures | Summer schools | Homogenizing | Convergence | Modeling and Simulation | Mathematics | Functional Analysis | Analysis of PDEs | Computer Science
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 7/2016, Volume 50, Issue 3, pp. 204 - 218
We study the convergence of continuous spectrum eigenfunctions for differential operators of divergence type with ε-periodic coefficients, where ε is a small... 
homogenization | double porosity model | Functional Analysis | Analysis | Bloch eigenfunction | Mathematics | Bloch principle | two-scale convergence | convergence of spectra | MATHEMATICS | MATHEMATICS, APPLIED | 2-SCALE CONVERGENCE | Porosity
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2015, Volume 13, Issue 3, pp. 1061 - 1105
Journal Article
Applicable Analysis, ISSN 0003-6811, 02/2015, Volume 94, Issue 2, pp. 375 - 398
We investigate the deformation of heterogeneous plastic materials. The model uses internal variables and kinematic hardening, elastic and plastic strain are... 
plasticity | homogenization | convex analysis | two-scale convergence | MATHEMATICS, APPLIED | 35B27 | 74Q10 | PRAGER MODEL | ELASTOPLASTICITY | VISCOELASTICITY | 74C05 | HYSTERESIS | MONOTONE-OPERATORS | Images | Plasticity | Mathematical models | Plastic deformation | Constraining | Homogenizing | Convergence | Strain
Journal Article
Journal of Elasticity, ISSN 0374-3535, 1/2014, Volume 114, Issue 1, pp. 69 - 84
This work focuses on performing the homogenization of the Nernst-Planck-Poisson system, in order to obtain an efficient modelling of the ionic transfer and... 
Electrocapillarity | 78A57 | 35K60 | 76Sxx | Mechanics | Homogenization | Automotive Engineering | 76M50 | Nernst-Planck-Poisson system | Two-scale convergence | Physics | 35K55 | MIGRATION | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | ADSORPTION | TRANSPORT | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CEMENT-BASED MATERIALS | POROUS-MEDIA | DIFFUSION | Convergence | Media | Elasticity | Models | Modelling | Homogenizing
Journal Article
Applicable Analysis: Homogenization and Qualitative Theory of Differential Equations dedicated to the memory of Vassily Vassilievich Zhikov, ISSN 0003-6811, 01/2019, Volume 98, Issue 1-2, pp. 64 - 90
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2010, Volume 59, Issue 2, pp. 427 - 457
Journal Article
Asymptotic Analysis, ISSN 0921-7134, 2015, Volume 91, Issue 3-4, pp. 341 - 371
In this paper we establish new homogenization results for stochastic linear hyperbolic equations with periodically oscillating coefficients. We first use the... 
Prokhorov and Skorokhod compactness results | homogenization | hyperbolic stochastic PDE | corrector result | two-scale convergence | MATHEMATICS, APPLIED | 2ND-GRADE FLUIDS | 2-SCALE CONVERGENCE | CONTINUUM | WAVE-EQUATIONS | DOMAINS | ASYMPTOTIC-BEHAVIOR
Journal Article
Multiscale Modeling and Simulation, ISSN 1540-3459, 2013, Volume 11, Issue 1, pp. 92 - 117
The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The... 
Plywood structures | Two-scale convergence | Nonperiodic microstructures | Locally periodic homogenization | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | non-periodic microstructures | BEHAVIOR | plywood structures | locally periodic homogenization | PHYSICS, MATHEMATICAL | PRINCIPLES | two-scale convergence
Journal Article
Asymptotic Analysis, ISSN 0921-7134, 2012, Volume 80, Issue 3-4, pp. 237 - 267
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial... 
weakly stochastic homogenization | two-scale expansion | PERIODIC HOMOGENIZATION | COEFFICIENTS | MATHEMATICS, APPLIED | ERROR ESTIMATE
Journal Article
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