We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of ue to the solution u of the homogenized problem u + (H) over bar (x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity (H) over bar and we estimate the corresponding rate of convergence.
Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs
CAMILLI, FABIO;
2009-01-01
Abstract
We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of ue to the solution u of the homogenized problem u + (H) over bar (x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity (H) over bar and we estimate the corresponding rate of convergence.File in questo prodotto:
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