710 research outputs found
Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
We study the averaging behavior of nonlinear uniformly elliptic partial
differential equations with random Dirichlet or Neumann boundary data
oscillating on a small scale. Under conditions on the operator, the data and
the random media leading to concentration of measure, we prove an almost sure
and local uniform homogenization result with a rate of convergence in
probability
Convergence Rates in L^2 for Elliptic Homogenization Problems
We study rates of convergence of solutions in L^2 and H^{1/2} for a family of
elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients
in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a
consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov
eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently
established uniform estimates for the L^2 Dirichlet and Neumann problems in
\cite{12,13}, are new even for smooth domains.Comment: 25 page
Convergence rates in homogenization of higher order parabolic systems
This paper is concerned with the optimal convergence rate in homogenization
of higher order parabolic systems with bounded measurable, rapidly oscillating
periodic coefficients. The sharp O(\va) convergence rate in the space
L^2(0,T; H^{m-1}(\Om)) is obtained for both the initial-Dirichlet problem and
the initial-Neumann problem. The duality argument inspired by
\cite{suslinaD2013} is used here.Comment: 28 page
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