Propagation of Smallness in Elliptic Periodic Homogenization

Periodic Homogenization of Elliptic Problems (Draft)

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 ...

Periodic homogenization of Dirichlet problem for divergence type elliptic operators

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A non-periodic and two-dimensional example of elliptic homogenization

Background. When studying the microscale behavior (beyond the reach of numerical solution methods) of physical systems, one is naturally lead to the concept of homogenization, i.e., the theory of the convergence of sequences of partial differential equations. The homogenization of periodic structures using the two-scale convergence technique is well-established due to the pioneering work by Gab...

Homogenization of a Periodic Degenerate Semilinear Elliptic Pde

In this paper a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novetly of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of Rd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion...