Title: Finite Element Approximation of Elliptic Homogenization Problems in Nondivergence-Form
Abstract:
In the first part of the talk, we use uniform $W^{2,p}$ estimates to obtain corrector results for periodic homogenization
problems of the form $A(x/\varepsilon) : D^2 u_{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition.
We then propose and rigorously analyze a numerical scheme based on finite element approximations for such
nondivergence-form homogenization problems. Finally, we extend our results for the numerical homogenization to the
case of nonuniformly oscillating coefficients. Numerical experiments demonstrating the performance of the scheme
are provided in the end. This is joint work with Yves Capdeboscq (Université de Paris, CNRS, Sorbonne Université, LJLL)
and Endre Süli (University of Oxford).
