Uniform bound and convergence for elliptic homogenization problems

Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems

In this work, we are concerned with the convergence of the multiscale finite element method (MsFEM) for elliptic homogenization problems, where we do not assume a certain periodic or stochastic structure, but an averaging assumption which in particular covers periodic and ergodic stochastic coefficients. We also give a result on the convergence in the case of an arbitrary coupling between grid ...

Convergence in L space for the homogenization problems of elliptic and parabolic equations in the plane

We study the convergence rate of an asymptotic expansion for the elliptic and parabolic operators with rapidly oscillating coefficients. First we propose homogenized expansions which are convolution forms of Green function and given force term of elliptic equation. Then, using local Lp-theory, the growth rate of the perturbation of Green function is found. From the representation of elliptic so...

Spectral convergence for high contrast elliptic periodic problems with a defect via homogenization

We consider an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients with period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of ‘order one’ size. The local perturbation of coefficients for such operator could result in emergence of localized waves eigenfunctions with corresponding eigenva...

Uniform Estimates in Two Periodic Homogenization Problems

We analyze two partial diierential equations that are posed on perforated domains. We provide a priori estimates, that do not depend on the size of the perforation: a sequence of solutions is uniformly bounded in a Sobolev space of regular functions. The rst homogeniza-tion problem concerns the Laplace-and the mean-curvature operator with Neumann boundary conditions. We derive uniform Lipschitz...

Periodic Homogenization of Elliptic Problems (Draft)