Convergence rates in homogenization of higher-order parabolic systems
Weisheng Niu, Yao Xu · Discrete and Continuous Dynamical Systems · 2018
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 $O(\varepsilon )$ convergence rate in the space $L^2(0, T; H^{m-1}(\Omega ))$ is obtained for both the initial-Dirichlet problem and the initial-Neumann problem. The duality argument inspired by [25] is used here.