I will report our recent effort on the construction of higher order numerical method for elliptic multiscale partial differential equations. An online-office method based on a local discrete least-squares reconstruction of the effective matrix is proposed. The reconstruction exploits the data retrieved from the solutions of the cell problems, which can be solved by spectral method to arbitrarily higher order. The error estimate of the proposed method is analyzed in the framework of heterogeneous multiscale method (HMM). Numerical examples that include 2d/3d elliptic problem with multiscale coefficients as well as problem posed on concave domain will be reported. This is a joint work with Y.F. Huang, R. Li and F.Y. Tang.
 

Pinging Ming is a Feng Kang distinguished professor of Institute of Computational Mathematics/Scientific Engineering, AMSS, Chinese Academy of Sciences. He is also the vice director of the Sate Key laboratory of Scientific and Engineering Computing. His main research interest is multi scale modeling and computation of solids. He was awarded by National Natural Science Foundation of China for Distinguished Young Scholars in 2014.