Multiscale and Projective Interpolation Method with High Accuracy for Two Point Boundary Value Problem with Small Periodic Coefficients

We study two point boundary value problem with small periodic coefficients. It is difficult to obtain the numerical solution of the problem with high accuracy by using finite element method directly. A multiscale finite element method with high accuracy and its error estimate are presented by using homogenization method and multiscale asymptotic expansion and projective interpolation. The rigorous proofs of the results are proposed. Numerical results are presented to illustrate the theoretical results.