Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients
نویسندگان
چکیده
منابع مشابه
Asymptotics for the Solutions of Elliptic Systems with Rapidly Oscillating Coefficients
A singularly perturbed second order elliptic system in the entire space is treated. The coefficients of the systems oscillate rapidly and depend on both slow and fast variables. The homogenized operator is obtained and, in the uniform norm sense, the leading terms of the asymptotic expansion are constructed for the resolvent of the operator described by the system. The convergence of the spectr...
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We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense we construct the leading terms of the asymptotics expansion for the resolvent of the operator described by the system. The convergence of the spectrum is est...
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We consider singularly perturbed second order elliptic system in the whole space with fast oscillating coefficients. We construct the complete asymptotic expansions for the eigenvalues converging to the isolated ones of the homogenized system, as well as the complete asymptotic expansions for the associated eigenfunctions.
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We develop the convergence analysis for a numerical scheme proposed for approximating the solution of the elliptic problem L u = − ∂ ∂xi aij(x/ ) ∂ ∂xj u = f in Ω, u = 0 on ∂Ω, where the matrix a(y) = (aij(y)) is symmetric positive definite and periodic with period Y . The major goal is to develop a numerical scheme capturing the solution oscillations in the scale on a mesh size h > (or h >> )....
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A new multiscale finite element method is presented for solving the elliptic equations with rapidly oscillating coefficients. The proposed method is based on asymptotic analysis and careful numerical treatments for the boundary corrector terms by virtue of the recovery technique. Under the assumption that the oscillating coefficient is periodic, some superconvergence results are derived, which ...
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2009
ISSN: 1061-0022
DOI: 10.1090/s1061-0022-09-01043-7