Error estimates in periodic homogenization with a non-homogeneous Dirichlet condition
نویسنده
چکیده
In this paper we investigate the homogenization problem with a non-homogeneous Dirichlet condition. Our aim is to give error estimates with boundary data in H1/2(∂Ω). The tools used are those of the unfolding method in periodic homogenization.
منابع مشابه
Interior error estimate for periodic homogenization
In a previous article about the homogenization of the classical problem of diffusion in a bounded domain with sufficiently smooth boundary we proved that the error is of order ε. Now, for an open set Ω with sufficiently smooth boundary (C) and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in Ω the error is of order ε. If the open set Ω⊂R is of ...
متن کاملA Nite Element Method for a Unidimensional Single-phase Nonlinear Free Boundary Problem in Groundwater Ow
Consider a unidimensional, single-phase nonlinear Stefan problem with nonlinear source and permeance terms, and a Dirichlet boundary condition depending on the free-boundary function. This problem is important in groundwater ow. By immobilizing the free-boundary with the help of a Landau type transformation, together with a homogeneous transformation dealing with the nonhomogeneous Dirichlet bo...
متن کاملW 1,p ESTIMATES FOR ELLIPTIC HOMOGENIZATION PROBLEMS IN NONSMOOTH DOMAINS
Let Lε = −div ` A ` x ε ́ ∇ ́ , ε > 0 be a family of second order elliptic operators with real, symmetric coefficients on a bounded Lipschitz domain Ω in Rn, subject to the Dirichlet boundary condition. Assuming that A(x) is periodic and belongs to VMO, we show that there exists δ > 0 independent of ε such that Riesz transforms ∇(Lε)−1/2 are uniformly bounded on Lp(Ω), where 1 < p < 3+δ if n ≥ 3,...
متن کاملError estimates for periodic homogenization with non-smooth coefficients
In this paper we present new results regarding the H1 0 -norm error estimate for the classical problem in homogenization using suitable boundary layer correctors. Compared with all the existing results on the subject, which assume either smooth enough coefficients or smooth data, we use the periodic unfolding method and propose a new asymptotic series to approximate the solution uε with an erro...
متن کاملEffective boundary condition at a rough surface starting from a slip condition
We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ǫ. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ε = 0 is always no-slip. We give in this paper error estimates for this homo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Asymptotic Analysis
دوره 87 شماره
صفحات -
تاریخ انتشار 2014