REDUCTION OF THE RESONANCE ERROR — PART 1: APPROXIMATION OF HOMOGENIZED COEFFICIENTS
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Publication:3098843
DOI10.1142/S0218202511005507zbMath1233.35016MaRDI QIDQ3098843
Publication date: 18 November 2011
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
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Cites Work
- Unnamed Item
- An optimal variance estimate in stochastic homogenization of discrete elliptic equations
- Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
- The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size
- The Green function for uniformly elliptic equations
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Approximations of effective coefficients in stochastic homogenization
- Improving on computation of homogenized coefficients in the periodic and quasi-periodic settings
- A homogenization result for planar, polygonal networks
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
- An Analytical Framework for the Numerical Homogenization of Monotone Elliptic Operators and Quasiconvex Energies
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