Convergence rates in almost-periodic homogenization of higher-order elliptic systems

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 Rates for the Stratified Periodic Homogenization Problems

In this paper, we study the convergence rates of homogenization problems for composites with general stratified periodic structure. After introduced auxiliary function, we get the representation formula satisfied by oscillatory solution and homogenized solution. Then we utilize the formula in combination with the asymptotic estimates of Green functions to obtain convergence rates in p L of solu...

Periodic Homogenization of Elliptic Problems (Draft)

On the Rate of Convergence in Periodic Homogenization of Scalar First-Order Ordinary Differential Equations

In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with rapidly oscillating coefficients, and the solution of the limiting homogenized equation. As an application of our result, we obtain an error estimate for the solut...

Multiscale Young Measures in Almost Periodic Homogenization and Applications

We prove the existence of multiscale Young measures associated with almost periodic homogenization. We give applications of this tool in the homogenization of nonlinear partial differential equations with an almost periodic structure, such as scalar conservation laws, nonlinear transport equations, HamiltonJacobi equations and fully nonlinear elliptic equations. Motivated by the application to ...