MultiScale Asymptotic Analysis Method with High Accuracy for the Second Order Elliptic Equation with Oscillating Periodic Coefficients in Perforated Domain

We consider the Neumman boundary value problem of second order elliptic equation with oscillating periodic coefficients in perforated domains. It is very difficult to solve the problem by using numerical methods directly, such as finite element method and finite difference method, due to the huge computing scaling. Using homogenization method, two-scale asymptotic expansion and projective interpolation, a high accuracy algorithm and its error estimate are reported. The rigorous proofs of the results are proposed. Finally, numerical example supports the theoretical results.